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Targeting at the problem of pavement cracking under longterm load, this study developed a newtype semirigid base layer structure based on the CGC (cement stabilized macadam  graded broken stone  cement stabilized macadam) combinations, and used ANSYS to simulate this proposed structure under conditions of different modulus combinations, deflection under different thickness, different vertical strain values on the top surface of roadbed, and different transverse tensile stress values of bottom base layer. The simulation results indicate that, the various mechanical properties of the proposed new structure can well meet the specifications, and the time of crack generation has been slowed down; the use of graded broken stone in the proposed structure has achieved both the purposes of saving construction cost and reducing construction difficulty. By reasonably controlling the CGC structure and modulus, this study has successfully suppressed the generation of reflection cracks, which can provide good theoretical evidence for prolonging the service life of semirigid base layer pavement.
asphalt pavement, finite element, reflection cracks, stress distribution, road performance
In China, more than 90% of road pavement structures adopted a semirigid base layer structure [1]. During the design process of semirigid asphalt base layer pavement, the elastic layered system theory is often used for the design and calculation of road structures. According to related research, the interlayer bonding state can affect the mechanical response of the pavement structure, poor interlayer bonding will degrade the performance of the pavement [2]. The semirigid asphalt base layer pavement has the properties of small deflection, high rigidity, and weak resistance to deformation, since its bottom base layer often bears a large tensile stress, the pavement can easily reach limit state and crack, and then the cracks will develop into reflection cracks [3]. In China, for most of the semirigid base layer pavement, before reaching the service life, its functions have already degraded and the structure has been damaged [4]. Combination analysis of the traditional semirigid base layer pavement suggests that it’s more reasonable to control the elastic modulus between 15003000Mpa and the thickness below 35cm [5], then, with the increase of the elastic modulus and thickness of the semirigid base layer, the change value of each indicator becomes smaller and smaller, so it’s meaningless to blindly increase the elastic modulus and thickness of the semirigid base layer. It is known that the graded crushed stone can fully absorb the strain energy released by cracks in the lower layer, in this way, it could suppress the generation of reflection cracks. In view of these facts, we propose a newtype interlayer combination, the CGC (cement stabilized macadam  graded broken stone  cement stabilized macadam) structure for the target problem in this paper. Then, the ANSYS software is used to simulate the interlayer state of the CGC structure, such as the stress and strain; through the research, we hope to reduce the thickness and cost as much as possible under the premise of meeting relevant specifications, so that the structure could exert a good role in suppressing reflection cracks.
2.1 Basic assumptions [6]
Following assumptions are usually made for elastic layered systems:
2.2 Structure of asphalt pavement
In ANSYS simulation, the influence of boundary size had been minimized as much as possible [7]. Therefore, the constructed semirigid asphalt base layer pavement model had a size of 10m×xm×10m, (length, height, and width), the pavement model was divided into 7 layers, from top to bottom, they are: top surface layer, middle surface layer, lower surface layer, top base layer, middle base layer, lower base layer, and soil base layer. Solid185 units were used to build the model, and there’re a total of 81608 units in the model, as shown in Figure 1.
Figure 1. Model of the pavement
2.3 Selection of material parameters
In terms of material selection, all layers in the model were elastic layered structures, the material parameters of each structure layer are listed in Table 1 below.
Table 1. Structure layers and material parameters of the pavement model [8]
Structure layer 
Thickness/cm 
Elastic modulus/Mpa 
Poisson’s ratio 
Asphalt top surface layer AC13 
5 
1200 
0.25 
Asphalt middle surface layerAC16 
5 
1450 
0.25 
Asphalt lower surface layerAC20 
10 
1950 
0.25 
Cement stabilized macadam 
10/5/10/5 
800/900/1000/1100/1200 
0.4 
Graded broken stone 
10/20/20/30 
300/340/380/420/460 
0.3 
Cement stabilized macadam 
10/5/10/5 
800/900/1000/1100/1200 
0.4 
Soil base 
 
60 
0.35 
2.4 Load selection
The standard axle load of the pavement was indicated by BZZ100, the value of axle load took 100KN, and the wheel pressure was 0.7Mpa [9, 10]. In this paper, based on the equivalent tire contact area, the shape of the contact area between the wheel and the ground was simplified into a rectangle with a length of 0.21m and a width of 0.167m, the distance between the centers of two wheels was 1.3m, see Figure 2.
Figure 2. Shape of the contact area between wheel and ground
2.5 Boundary conditions
To simulate real pavement conditions, it’s necessary to set boundary conditions for the pavement model. In the Y direction, namely the structure depth direction, the bottom position was fixed; there’s no displacement on the left and right sides of X direction, namely the driving direction; and there’s no Zdirection displacement on both sides of the cross section.
3.1 Vertical strain of the top surface of roadbed
The allowable vertical compressive strain on the top surface of roadbed was calculated by Formula 1.
[εz]=1.25×1040.1β (kT3Ne4)0.21 (1)
where,
[εz] is the allowable vertical compressive strain on the top surface of roadbed (106);
β is the reliability index, according to the highway grade, its value took 1.28 in this paper;
Ne4 is the cumulative number of equivalent design axle loads on the designed lane within the designed service life, its value was 12000000;
kT3 is the temperature adjustment coefficient, its value took 1.129;
After calculation, it’s obtained that εz =0.29595×103.
3.2 Transverse tensile stress of the bottom base layer
Table 2. Allowable tensile stress of structure layers
Structure layer 
Allowable tensile stress/Mpa 
Asphalt pavement layer 
0.465 
Base layer 
0.323 
Bottom base layer 
0.087 
The HPDS pavement design software allows users to design highways of different grades according to the latest highway design specifications, the purpose of this software is to alleviate the workload of constructors, reduce errors in manual calculations, and make the various grades of highways be more in line with national standards. After inputting the structure layers of the pavement and their elastic modulus values into the software, the output calculated allowable tensile stress of the bottom base layer was 0.087 MPa (Table 2).
4.1 Deflection value
Deflection is caused by the deformation of each structure layer of the pavement when the road surface is subject to a load, it can reflect the loadbearing capacity of each structure layer, to a certain extent, it can also reflect the use state of the road. A toolarge deflection value indicates that the loadbearing capacity of each structure layer is insufficient, and the road’s ability to resist damages will weaken gradually, under the comprehensive effects of external factors such as traffic loads, and climate and environment conditions, a series of diseases will occur to the road. Therefore, deflection is a very important indicator for studying the different pavement structures [11], and the deflection values of pavements with different thickness and modulus obtained through simulation are given in Table 3.
Figure 3. Deflection of the pavement under conditions of different modulus combinations and a base layer thickness of 300 mm
Figure 4. Deflection of the pavement under conditions of different modulus combinations and a base layer thickness of 400 mm
Figure 5. Simulation of the deflection of 100+100+100 pavement
Table 3. Deflection of pavements with different structures and modulus values
Base layer structure 
Different modulus combinations/Mpa 
Maximum deflection of road surface/mm 
100+100+100 
800+300+800 
0.172 
900+340+900 
0.165 

1000+380+1000 
0.160 

1100+420+1100 
0.156 

1200+460+1200 
0.152 

50+200+50 
800+300+800 
0.191 
900+340+900 
0.183 

1000+380+1000 
0.177 

1100+420+1100 
0.171 

1200+460+1200 
0.167 

100+200+100 
800+300+800 
0.191 
900+340+900 
0.183 

1000+380+1000 
0.176 

1100+420+1100 
0.171 

1200+460+1200 
0.166 

50+300+50 
800+300+800 
0.208 
900+340+900 
0.199 

1000+380+1000 
0.191 

1100+420+1100 
0.184 

1200+460+1200 
0.179 

200+100+100 
800+300+800 
0.173 
900+340+900 
0.167 

1000+380+1000 
0.161 

1100+420+1100 
0.157 

1200+460+1200 
0.153 

100+100+200 
800+300+800 
0.178 
900+340+900 
0.171 

1000+380+1000 
0.166 

1100+420+1100 
0.161 

1200+460+1200 
0.157 
The deflection of different base layer structures with different elastic modulus values was simulated using the constructed model, and the obtained values showed that, under each structure, the displacement of road surface had met the specifications. Under the condition that the thickness of the base layer was 300mm, the pavement deflection values of different base layer structures had all met the specifications (Figure 3, Figure 4). With the increase of modulus, the pavement deflection values decreased gradually (Figure 5). In case of the 50+200+50 base layer structure, when the modulus combination changed from 800+300+800 to 1200+460+1200, the maximum deflection of the pavement was 0.191mm, the minimum deflection of the pavement was 0.167mm, the deflection value of the pavement had reduced by 12.6%. In case of the 100+100+100 base layer structure, when the modulus combination changed from 800+300+800 to 1200+460+1200, the maximum deflection of the pavement was 0.172mm, the minimum deflection of the pavement was 0.152mm, the deflection value of the pavement had reduced by 11.6%. After analyzing the data, it’s found that under a same thickness, the thicker the cement stabilized macadam, the smaller the pavement deflection value. Under the condition that the thickness of the base layer was 400mm, the pavement deflection of different base layer structures had all met the specifications. With the increase of modulus, the pavement deflection values decreased gradually. In case of the 50+300+50 base layer structure, when the modulus combination changed from 800+300+800 to 1200+460+1200, the maximum deflection of the pavement was 0.208mm, the minimum deflection of the pavement was 0.179mm, the deflection value of the pavement had reduced by 13.9%. In case of the 200+100+100 base layer structure, when the modulus combination changed from 800+300+800 to 1200+460+1200, the maximum deflection of the pavement was 0.173mm, the minimum deflection of the pavement was 0.153mm, the deflection value of the pavement had reduced by 11.6%. In case of the 100+100+200 base layer structure, when the modulus combination changed from 800+300+800 to 1200+460+1200, the maximum deflection of the pavement was 0.178mm, the minimum deflection of the pavement was 0.157mm, the deflection value of the pavement had reduced by 11.8%. After analyzing the data, it’s found that under a same thickness, the thicker the cement stabilized macadam, the smaller the pavement deflection value. In case of a same base layer structure, if the cement stabilized macadam is placed in the bottom base layer, the deflection value of the pavement will increase slightly.
4.2 Tensile stress at the bottom of bottom base layer
Figure 6. Tensile stress at the bottom of bottom base layer under the conditions of different modulus combinations and a base layer thickness of 300 mm
Figure 7. Tensile stress at the bottom of bottom base layer under the conditions of different modulus combinations and a base layer thickness of 400 mm
When the tensile stress at the bottom of bottom base layer is greater than the allowable tensile stress at the bottom of the base layer, cracks will appear in the base layer, and to a certain extent, the growth speed the cracks spreading to the surface layer is determined by the thickness of the base layer, namely the structure combination of the base layer (Figure 6, Figure 7). The toothick base layer will greatly increase the construction cost of the pavement, during construction, it’ll be difficult to compact the pavement, moreover, after putting into real use, the pavement is prone to wheel rutting and other damages, which will seriously affect the quality of the pavement (Figure 8). If the thickness of the base layer is too small, the bottom layer stress is not obvious, therefore, a good choice of base layer structure combination can prevent the generation of cracks. According to the results of finite element analysis shown below, it’s obtained that the base layers of different modulus combinations had also met the specifications of tensile stress at the bottom of base layer in Table 4.
Figure 8. Tensile stress at the bottom of bottom base layer of the 100+100+100 pavement
Table 4. Vertical compressive strain on the top surface of roadbed with different base structure types
Base layer structure 
Different modulus combinations/Mpa 
Tensile stress at the bottom of bottom base layer/Mpa 
100+100+100 
800+300+800 
0.021188 
900+340+900 
0.021894 

1000+380+1000 
0.022511 

1100+420+1100 
0.023057 

1200+460+1200 
0.023545 

50+200+50 
800+300+800 
0.02167 
900+340+900 
0.025509 

1000+380+1000 
0.023249 

1100+420+1100 
0.023908 

1200+460+1200 
0.024502 

100+200+100 
800+300+800 
0.015931 
900+340+900 
0.016371 

1000+380+1000 
0.016755 

1100+420+1100 
0.017094 

1200+460+1200 
0.017396 

50+300+50 
800+300+800 
0.016455 
900+340+900 
0.016957 

1000+380+1000 
0.017396 

1100+420+1100 
0.017784 

1200+460+1200 
0.01813 

200+100+100 
800+300+800 
0.016358 
900+340+900 
0.016742 

1000+380+1000 
0.017073 

1100+420+1100 
0.017363 

1200+460+1200 
0.017619 

100+100+200 
800+300+800 
0.017111 
900+340+900 
0.017525 

1000+380+1000 
0.017882 

1100+420+1100 
0.018194 

1200+460+1200 
0.018471 
With the help of the constructed model, the tensile stress at the bottom of bottom base layer under different base layer structures and different elastic modulus values were simulated, and the results showed that for each structure type, the tensile stress at the bottom of bottom base layer had all met the specifications. After analyzing the data, it’s concluded that, under a same thickness, the thicker the cement stabilized macadam, the smaller the tensile stress at the bottom of the bottom base layer of the pavement. The thicker the graded crushed stone, the higher the growth rate of tensile stress at the bottom of the bottom base layer. Under the condition of a same type of base layer structure, if the cement stabilized macadam is placed in the bottom base layer, the tensile stress at the bottom of the bottom base layer of the pavement will increase slightly.
4.3 Vertical compressive strain on the top surface of roadbed
Figure 9. Vertical compressive strain on the top surface of roadbed under the conditions of different modulus combinations and a base layer thickness of 300 mm
Figure 10. Vertical compressive strain on the top surface of roadbed under the conditions of different modulus combinations and a base layer thickness of 400 mm
The obtained values showed that, under each structure, the vertical compressive strain on the top surface of roadbed had all met the specifications. After analyzing the data, it’s concluded that, under a same thickness, the thicker the cement stabilized macadam, the smaller the vertical compressive strain on the top surface of roadbed (Figure 9, Figure 10). The thicker the graded broken stone used in the pavement, the lower the growth rate of vertical compressive strain on the top surface of roadbed. Under the condition of a same type of base layer structure (Figure 11), if the cement stabilized macadam is placed in the bottom base layer, the vertical compressive strain on the top surface of roadbed will increase slightly in Table 5.
Table 5. Vertical compressive strain on the top surface of roadbed under different base layer structures
Base layer structure 
Different modulus combinations/Mpa 
Vertical compressive strain on the top surface of roadbed 
100+100+100 
800+300+800 
8.37e5 
900+340+900 
7.64e5 

1000+380+1000 
7.04e5 

1100+420+1100 
6.53e5 

1200+460+1200 
6.09e5 

50+200+50 
800+300+800 
6.72e5 
900+340+900 
6.14e5 

1000+380+1000 
5.67e5 

1100+420+1100 
5.26e5 

1200+460+1200 
4.92e5 

100+200+100 
800+300+800 
5.6e5 
900+340+900 
5.11e5 

1000+380+1000 
4.7e5 

1100+420+1100 
4.36e5 

1200+460+1200 
4.07e5 

50+300+50 
800+300+800 
4.76e5 
900+340+900 
4.34e5 

1000+380+1000 
4.0e5 

1100+420+1100 
3.71e5 

1200+460+1200 
3.46e5 

200+100+100 
800+300+800 
6.02e5 
900+340+900 
5.47e5 

1000+380+1000 
5.02e5 

1100+420+1100 
4.63e5 

1200+460+1200 
4.31e5 

100+100+200 
800+300+800 
6.25e5 
900+340+900 
5.69e5 

1000+380+1000 
5.22e5 

1100+420+1100 
4.83e5 

1200+460+1200 
4.49e5 
Figure 11. Vertical compressive strain on the top surface of roadbed of the 100+100+100 pavement
By conducting numerical simulation on base layer structures of different thickness and modulus combinations, this paper obtained a newtype pavement structure, the CGC structure. Simulation data showed that, the proposed structure had met relevant specifications in terms of deflection value, tensile stress at the bottom of bottom base layer, and vertical strain on the top surface of roadbed. In engineering projects in the future, by reasonably controlling the CGC structure and modulus of the pavement, the design ideas of suppressing crack generation and optimizing pavement structure could be realized, which has a certain reference value for the structure design of asphalt pavement.
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