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The various damages of asphalt pavement are closely related to the mesomechanical gradual behavior of asphalt materials, and it is very important to study the mesoscopic response under vibration loading in order to reveal the failure mechanism of asphalt pavement. The semisinusoidal vertical load is applied to the subgrade-surface discrete element model in this paper, and we use the model to analyze the evolution behavior of microcrack generation and expansion processes, stress distribution and stress transfer, and displacement field in various structural layers of asphalt pavement. The results show that the number of cracks increases rapidly on both sides of the vibration load, the rut is generated due to repeated load on the wheel, the asphalt mixture has bulging phenomenon on both sides of the rut and formed macroscopic cracks at the ridge, the microcracks extend mainly along the weak joints of the edges of the coarse aggregate and the asphalt cement, the number of microcracks increases slowly at the initial stage of the vibration load, the microcracks increase sharply until macroscopic cracks appear with the vibration load increases, the direction of compressive stress extends parallel to the microcrack, and the direction of tensile stress extends perpendicular to the microcracks inside the asphalt pavement. The results show that the discrete element method can not only obtain the stress and displacement of each structural layer, but also reveal the microcrack gradual behavior between particle flows.

Asphalt pavement is generally composed of an asphalt layer, a cement stabilized layer, and a road base layer; the asphalt layer is mainly composed of asphalt, coarse aggregate, fine aggregate, and mineral powder; the cement stabilizing layer is composed of coarse aggregate, fine aggregate, and cement; the roadbed is mainly composed of earth and stone [

Macroscopic mechanics often adopts the traditional continuum mechanics theory, which assumes that the structural layers inside the subgrade are the same homogeneous body, and the geometric and physical characteristics, such as aggregate shape, spatial position, aggregate texture, and aggregate gradation, are ignored; however, the internal geometry and physical properties are of great importance to the overall performance of the pavement structure layer [

In this paper, according to the actual pavement structure hierarchy, and using the combination of the random placement algorithm and porosity treatment principle, the two-dimensional subgrade-pavement discrete element model is established by using the FISH language in the PFC2D software and the mesoscopic parameters of each structural layer are obtained by comparing the standard uniaxial compression stress-strain test of materials with the uniaxial compression test of the established model. Semisinusoidal vertical load is applied to simulate vehicle loading and unloading; reveal the relationship between the microcrack propagation process, mesoscopic failure, and the macroscopic dynamic response of each structural layer; and analyze the mesoscopic response gradation behavior of asphalt pavement under vibration loading; these research results provide a reference for the mechanism of pavement damage.

According to the literature research [

Pavement structural parameters.

Material name | Depth (cm) | Structural layer location |
---|---|---|

SMA-13 | 4 | Upper layer |

AC-20 | 11 | Lower layer |

5% cement stabilized gravel | 16 | Upper base layer |

5% cement stabilized gravel | 16 | Lower base layer |

4% cement stabilized grit | 18 | Bottom base layer |

Earth and stone | 100 | Subgrade |

A variety of common contact models are provided in the PFC2D software. The linear parallel bond model can reflect the internal mechanical relationship between the binding material and the coarse aggregate, and parallel bonding model calculation is relatively simple [

Linear parallel bond model. (a) Mechanical relationship between particles. (b) Mechanical relationship of linear parallel bond model.

Figures

We have corresponding force and bending moment increment when the particles are displaced:

In these equations,

Force and bending moment are updated according to the following formula where

So, we can obtain normal stress and tangential stress:

In the particle flow calculation process, the contact force and the unbalanced force are constantly balanced in the particle flow motion; microcracks are generated between particles when the tensile and shear resistance exceeds the bond strength in the model [

According to the theory of asphalt cement, the coarse aggregate (particle size greater than 2.36 mm) plays a skeleton role and bears most of the internal stress in the asphalt mixture, and the fine aggregate (particle size less than 2.36 mm) plays the role of filling skeleton space and binding between the coarse aggregates. In order to simplify the model and simplify the calculation data, we consider fine aggregate, water, and asphalt as binding materials, so the discrete element model only contains coarse aggregate and binding material particles [

Six spaces are generated and separated by walls using the PFC2D software, according to the actual structural material grading, the distribution area of the coarse aggregate is calculated and placed it in the wall step by step. The specific model is shown in Figure

Discrete element model of subgrade and pavement structure.

The two-wheel set BZZ-100 is used as the standard load in the pavement design specification, the tire marks are actually elliptical; however, for the convenience of calculation, more circular tire marks are used in the model calculation, the tire load is regarded as the equivalent circular uniform load, and the internal pressure of the tire is used instead of the contact pressure at the bottom of the wheel. The specific values are shown in Table

Design parameters of standard axle load.

Load name | Standard axle load, P (kN) | Ground tire pressure, P (MPa) | Equivalent circle diameter of single wheel pressure transmitting surface (cm) | Tire center distance (cm) |
---|---|---|---|---|

BZZ-100 | 100 | 0.7 | 21.3 | 1.5 d |

To simulate wheel load with CLUMP unit on the surface layer above the model, five PEBBLE units are used to represent one wheel, five PEBBLE units are tightly connected (21.3 cm in diameter), and the distance is 10.65 cm between the two CLUMP units (the upper layer of Figure

Amplitude curve of vibration load.

In the literature, most experts and scholars believe that the macroscopic mechanical parameters cannot be directly applied to the discrete element model [

Stress-strain data of SMA-13 asphalt mixture.

Single-axial compression failure model of SMA-13 asphalt mixture: (a) initial load model; (b) medium load model; (c) final load model.

Single-axial compression test of SMA-13 type asphalt mixture: (a) initial compression stage; (b) medium compression stage; (c) final compression phase; (d) terminal compression crack.

It is necessary to know the mesoscopic parameters (

Microscopic parameters of linear parallel bond model in the asphalt mixture.

Structural layer location | Particle density (kg·m^{−3}) |
Stiffness ratio between tensile and shear, |
Tensile strength, |
Cohesion, |
Particle elastic modulus, |
Particle radius (mm) | |
---|---|---|---|---|---|---|---|

Upper layer | Coarse aggregate | 2500 | 1 | 4.2 |
2.3 |
6.3 |
0.5–0.75 |

Binding material particles | 2100 | 1 | 4.4 |
5.2 |
5.9 |
0.5–0.75 | |

Lower layer | Coarse aggregate | 2500 | 0.8 | 6.1 |
1.85 |
6.5 |
0.75–1 |

Binding material particles | 2100 | 0.8 | 5.4 |
6.2 |
7.8 |
0.75–1 | |

Upper base layer | 2400 | 1 | 8.3 |
9.7 |
4.3 |
0.75–1 | |

Lower base layer | 2400 | 1 | 6.9 |
8.1 |
4.4 |
0.75–1 | |

Bottom base layer | 2200 | 1 | 6.4 |
8.43 |
3.2 |
0.75–1 | |

Subgrade | 1900 | 1 | 1.5 |
5.4 |
6.4 |
0.5–1 |

Applying a half-wave sinusoidal vertical load to the surface of the model, and gradually generating microcracks inside the pavement, microcrack density continues to increase with the load continues; finally, the microcracks penetrate each other to form macrocrack. Figures

Microcrack shape in 1 second.

Microcrack shape in 2 seconds.

Microcrack shape in 4 seconds.

Microcrack shape in 12 seconds.

It can be seen from Figure

It can be seen from Figure

It can be seen from Figure

It can be seen from Figure

By studying the whole process of microcrack propagation, it can be known that most of the microcracks expand along the shear stress direction under the double-wheel load, the number of microcracks is the highest at both ends of the load, the shape of microcracks is symmetrically distributed overall, and the microcrack density in the middle strong stress region of the load is much larger than the microcrack density at both ends of the load.

Figure

Macrocrack shape in 4 seconds.

Figures

Local macrocrack extension of the upper surface layer.

Local macrocrack extension of the lower surface layer.

From the trend of microcrack generation and expansion, it is known that the combination is the main weak part of asphalt mixture between coarse aggregate and asphalt cement, which is easy to produce early microcracks; microcracks eventually become macroscopic cracks under continuous vehicle loading. Functional conditions have already appeared in the pavement structure in this state, and we should protect it.

Figure

Relation curve of microcrack number and load time.

It can be seen from the above figure that there is almost no microcrack inside the 0-1 s phase discrete element model, stress is continuously transmitted between the particles, and the stress continues to accumulate and self-adjust, eventually reaching dynamic equilibrium. A small number of microcracks appear inside the 1 s-2 s stage discrete element model, and the number of microcracks is very small, most of the macroscopic physical and mechanical performance indicators are not damaged in this state. The number of microcracks increases rapidly inside the 2 s–8 s stage, and the length of microcracks continued to increase. The number of microcracks is linear with the load time. The dynamic balance of the model is broken at this stage. Microcracks do not appear randomly, but spread rapidly downwards and outwards on both sides of the tire. Most of the microcracks cross each other and merge in this state, and the surface layer shows macroscopic cracks. The ability to resist external loads is much reduced in the model, and the rutting is gradually increasing. The number of microcracks is in a stationary phase inside 8 s–10 s stage, and the number of microcracks does not increase significantly. The number of microcracks has a certain increasing trend during the 10 s–12 s stage, but the rate of growth is small.

Due to external wheel vibration load, increasing microcracks have seriously changed the ability to withstand external loads; if the model is subjected to wheel loads for a long time, the particle flow cannot be completely restored to its original state, and the asphalt pavement is already in an initial destruction state.

Since the discrete element model is a point contact between particles, the particle flow will continue to shift and rotate under the continuous vibration load of the wheel, stress is transmitted between the particles, and the change of stress reflects the macroscopic structural mechanical properties in the discrete element model. The stress is closely related to the microcracks generation, microcracks expansion, and microcracks penetration in particles.

Figure

Internal force chain diagram of the whole model.

Figure

Force chain diagram near the crack in the upper layer.

Figure

Force chain diagram of crack location in the lower layer.

The particle flow will continue to shift and rotate under the continuous vibration load of the wheel, and the appearance of the model shows that the particles have a tendency to move around.

Figure

Overall displacement nephogram of discrete element model.

Figure

Horizontal displacement nephogram of discrete element model.

Figure

Vertical displacement nephogram of discrete element model.

By comparing the indoor standard uniaxial compression test with the discrete element model, we can obtain the mesoscopic parameters of each structural layer and establish a discrete element model of the pavement structure and the mesoscopic response gradual behavior of the pavement under the given vibration load. The results show that the initial crack growth is slow in the particle flow under the action of vibration load and the crack growth is faster in the later stage, which eventually leads to rutting on the surface of the model. Most of the cracks extend along the shearing direction in the particle streams, and there are many cracks at the bottom of the wheel, and the cracks are almost symmetrically arranged. Most of the fine cracks extend along the edge of the coarse aggregate and the weakness of the asphalt cement in the particles under the action of vibration load; eventually, microcracks merge into macroscopic cracks in different directions. The force chain pattern is “U” type in the particles under the action of vibration load, which has both compressive and tensile stresses. The upper layer and the lower layer mainly exhibit tensile stress, and the other regions exhibit compressive stress; the particles are completely separated on both sides of the crack. The upper layer particles have the largest displacement under the action of vibration load, the displacement gradually decreases with road depth increases, and the subgrade has almost no displacement. The horizontal displacement layer has obvious boundary and has a tendency toward both sides, and the horizontal displacement is symmetrically arranged; the particle flow has a bulging phenomenon on both sides of the rut area. The discrete element model can not only obtain the stress and displacement under the action of vibration load, but also obtain the variation trend between the particles; the discrete element model can express both macroscopic mechanical behavior and mechanical mesoscopic behavior.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare no conflicts of interest.

Z.Y. and E.C. conceived the algorithm and designed experiments; Z.W. implemented the experiments and processed test data; and C.S. analyzed the results. All authors read and revised the manuscript.

This research was funded by the National Natural Science Foundation of China (grant 11172183) and Central Guided Local Science and Technology Development Project of China (18242219G).