Parameter Optimization of Graded Macadam Transitional Layer for Inverted Asphalt Pavement Based on the Mechanical Response and Strength Standard

School of Energy and Architecture, Xi’an Aeronautical University, No. 259 Eastern Erhuan Road, Xi’an 710077, Shaanxi, China Key Laboratory for Special Area Highway Engineering of Ministry of Education, Chang’an University, Middle Section of South Erhuan Road, Xi’an 710064, Shaanxi, China Key Laboratory of Geological Hazards on 0ree Gorges Reservoir Area, China 0ree Gorges University, No. 8 University Road, Yichang 443002, Hubei, China


Introduction
Under the continuous effect of heavy traffic, the traditional pavement structure design method based on the multilayer elastic theory analysis is facing a severe challenge. It is embodied in the following aspects: (1) the mechanical indexes considered are mainly tensile stress and compressive stress, which are too simple to analyze the damage mechanism of the current road under the complex traffic and climate condition. (2) e structural combination design does not adequately consider the mechanical response and material properties.
ese challenges lead to a terrible decrease in the durability of asphalt pavement. erefore, road engineers have conducted many related studies. Karimi et al. developed an anisotropic nonlinear viscoelastic constitutive relationship that is sensitive to the tension/compression stress mode by extending Schapery's nonlinear viscoelastic model [1]. Wang et al. conducted a combined static-and-dynamics analysis to evaluate the pavement structure stress state comprehensively [2]. Lv et al. established a normalization model of fatigue characteristics for asphalt mixtures under different stress states based on the yield criterion in 3-dimensional stress states [3]. Lytton et al. addressed the measurement and modelling of the damaged properties of asphalt mixtures, including the fracture, healing, and viscoelastic deformation of the asphalt mixtures in tensile and compressive loading [4]. Si et al. built a finite element model of asphalt pavement using the software ABAQUS, which was used to analyze the thermal stress and pore water pressure in pavement structure under the condition of rainfall infiltration [5]. Behnke et al. investigated the structural long-term response of asphalt pavements (modeled as elastoplastic solid at large strains) under periodic traffic load by means of the finite element method (FEM) [6]. Assogba et al. examined the response of asphalt pavements to the combined effect of the nonlinear thermal gradient and the moving axle load by means of an advanced 3D pavement FE modelling [7]. Xie et al. analyzed the mechanical response of transverse cracks treatment in different geometrical structures under wheel load and temperature load based on the orthogonal design method [8]. All in all, various measures, such as nonlinear viscoelastic model, static-and-dynamics analysis, finite element model, and structural long-term response analysis, were used to improve the durability of the asphalt pavement. At present, each structural layer of asphalt pavement was basically designed according to the full functional requirements. Hence, it is difficult to adapt to the mechanical and functional requirements of the various structural layers of asphalt pavement [9]. For example, the upper layer mainly plays a role in the antirutting function, which means the asphalt mixture in the upper layer should have high strength. However, the resistance to cracking is also emphasized in the asphalt mixture design. In general, it is inevitably a challenge to balance the two performances mentioned above [10]. Inverted asphalt pavement (IAP) refers to a new type of asphalt pavement structure with graded gravel or asphalt stabilized gravel layer upon semirigid layer.
is kind of pavement structure can effectively enhance the antirutting ability and the resistance to crack of asphalt pavement [11]. In the cold region, the main distress types of the IAP structure with graded macadam transitional layer (GMTL) are cracking in the surface layer, rutting, and shear failure in the base layer [12]. e shear failure of GMTL is essentially related to the shear deformation caused by the excessive shear stress in the structure. erefore, the shear strength reflecting the shear deformation ability should be used as the strength control index. For the control index of shear strength of GMTL materials, scholars in China and other countries have done a lot of related researches. Lima proposed some new parameters of the Guimarães model and pointed out the necessity of granulometric distribution analysis to the stone skeleton in the granular base layer and the subbase layers [13]. Guo et al. made an analysis on the control  indicators based on the damage form of the graded crushed  stone (GCS) layer of the flexible asphalt pavement structure. e result showed that 10 cm thickness of asphalt surface is a turning point of change curve for the tensile stress indicator of the asphalt layer and the shear stress indicator of the graded macadam layer [14]. Han et al. adopted BISAR 3.0 program to calculate the shear stress in the graded crushed stone base. It is found that the asphalt layer should not be too thin when the thickness of the graded crushed stone base is 20 cm [15]. Xu et al. developed a plastic deformation model for the GCS base layer based on the relationship between relative deformation and plastic deformation ratio [16]. Although the proposed index can characterize the shear deformation resistance of flexible base materials, it is hard to be applied in practice because of the complex test process, the high test cost, and the inconsistent test methods.
To improve the durability of asphalt pavement with heavy traffic conditions in cold regions, the parameter optimization of GMTL for IAP based on the materials mechanical response and strength standard was conducted in this study.

Determination of Calculation Parameters for BISAR 3.0.
Based on the BISAR3.0 program, the stress, strain, and displacement of any point in the pavement structure under different layer contact conditions can be calculated, which provides data to quantitatively describe the mechanical response of the pavement structure [17]. Taking a large amount of mechanical calculation into consideration, the BISAR3.0 program was used to calculate the stress of asphalt pavement structure. e influence of the material parameters and the load changes of asphalt pavement structure on the structural stress was analyzed. During the analysis process, the pavement structure was usually regarded as a linear elastic layer system [18]. e structure and calculation parameters of the typical IAP are shown in Table 1.
e selected pavement structure type is derived from an IAP structure test section in the cold region of Hebei, China. According to the "Specifications for Design of Highway Asphalt Pavement (JTD D50-2017)," the load and calculation points are calculated using the double circular uniform vertical load [19], as shown in Figure 1.

Selection of Strength Control
Index. According to the damage characteristics of GMTL of IAP in cold regions, the strength control index is proposed combined with California Bearing Ratio (CBR), compressive strength (R c ), and the spatial attitude angel of aggregate obtained from a selfdeveloped real-time data acquisition and processing system (RDAPS). RDAPS with small volume, low cost, and high precision is developed in this study. e system consists of wireless intelligent attitude aggregate (WIAA), analysis software, and hardware equipment, as shown in Figure 2.
As seen from Figure 2(a), the WIAA with a size of 20 mm consisted of an attitude sensor, micropower supply module, and wireless transmission module (transmitter). WIAA is encapsulated by the hardened resin material using 3D printing technology. Hence, the shape of WIAA can be designed and controlled by the user. e signal stability is also acceptable due to the high mechanical strength of the WIAA shell. e micropower supply module has the function of a remote switch. e data acquisition interval can be controlled by software programming to ensure the long-term endurance of WIAA. e WIAA can output the data of the spatial attitude angle in three directions. From Figure 2(b), the software is developed by Python programming language. e aggregate attitude data can be collected, saved, and analyzed in real time. As shown in Figure 2(c), it mainly includes a wireless transmission module acting as a signal receptor, a micropower supply module acting as a control terminal, a data processing system, and a display screen. When the WIAA is implanted into GMTL, it can cooperate with graded macadam in deformation. e attitude angle of WIAA is collected and analyzed via the RDAPS, so as to quantitatively characterize the embedded state of graded macadam.
CBR can be used to characterize the load-bearing capacity and deformation resistance of materials. Moreover, the instrument used for the CBR test is convenient to operate. In case of an uneven settlement of pavement structure, R c can be used as an index to control the deformation of GMTL. During the compaction process of the graded macadam, the spatial attitude angle of WIAA would keep constant once the graded macadam is already in a dense state. In other words, the interlock skeleton was formed in the graded macadam. erefore, CBR, R c , and the attitude angle of WIAA are selected as strength design indexes of GMTL materials in this study.

Research Process.
Firstly, the stress distribution laws of GMTL were studied with different loads by means of BISAR3.0. e influences of the thickness and the modulus of GMTL on the pavement stress were analyzed and the optimal thickness and modulus range of the GMTL was determined. en, combined with the self-developed RDAPS, the strength control standard of the GMTL was established. Finally, the performance of the optimized IAP structure was verified through the MEPDG design method.
is study has practical significance for promoting the development of IAP construction technology in cold regions and improving the durability of asphalt pavement. e research flow chart is shown in Figure 3 [20].

Tensile Stress and Shear Stress of Asphalt Surface Layer.
e distribution of shear stress and the tensile stress of the asphalt surface layer under 0.7 MPa load are shown in Figure 4. Figure 4(a) shows that most of the large shear stress was seen in the range of 0 cm to 12 cm below the road surface. Among them, the maximum shear stress in the upper layer of the asphalt pavement was observed at L 5 point, about 4 cm from the road surface. e maximum shear stress in the middle layer appeared at L 4 point, 8 cm from the road surface. erefore, L 4 point and L 5 point were chosen as the research point for the shear stress of the asphalt surface layer. Figure 4(b) shows that tensile stress occurring at the L 1 and the O points, and the maximum tensile stress at the bottom of the asphalt layer appeared at the O 2 point. e O and the O 2 points were selected as the calculation points for studying the tensile stress of the asphalt pavement surface and the asphalt layer, respectively.

Shear Stress of GMTL.
For the asphalt pavement with GMTL, the tensile stress of the pavement surface is small even under heavy traffic load. e tensile stress of pavement surface was not considered under the traffic load if GMTL were designed [21]. Since GMTL was prone to plastic deformation, the shear stress distribution law of the GMTL under 0.7 MPa load was studied, as shown in Figure 5. Figure 5 shows that the maximum shear stress of the GMTL appeared at the O 2 point. Hence, the O 2 point was selected as the study point. e shear stress distribution of the O 2 point under different loads is shown in Figure 6. It can     Advances in Materials Science and Engineering be seen from Figure 6 that the maximum shear stress of the GMTL increases linearly with an increase in load.

Tensile Stress of Cement Stabilized Macadam Base
Layer. e tensile stress distribution law of cement stabilized macadam base layer under 0.7 MPa load is shown in Figure 7.  Figure 8, which shows that the maximum tensile stress at the bottom of the cement stabilized macadam base layer increases linearly with an increase in load.

Effect of GMTL on Mechanics Index of Each Structural
Layers. In order to facilitate calculation and analysis, the thickness range of GMTL is 12∼20 cm and the modulus range is 300∼800 MPa. e influences of the thickness and the modulus of GMTL on the tension stress at bottom of the surface layer, the maximum shear stress in GMTL, and the maximum tension stress in the semirigid base layer are shown in Figures 9-11. According to Figure 9, when the modulus of GMTL varies from 300 MPa to 800 MPa, the maximum tensile stress    at the bottom of the surface layer reduced by as high as 58%.
When the thickness of GMTL is unchanged while the modulus is 700 MPa, the tension stress at the bottom of the surface layer was the smallest. When the modulus of GMTL was 300 MPa, the tensile stress at the bottom of the surface layer increased significantly. However, the increasing trend of the tensile stress got weakened with an increase in modulus. Figure 10 shows that when the thickness of GMTL is unchanged, the shear stress of GMTL increases as high 17% with an increase in modulus. When the thickness of GMTL is 18 cm, the self-shear stress is relatively minimum. Figure 11 shows that when the thickness of GMTL is constant, the change in modulus of GMTL has no significant effect on the tensile stress at bottom of the semirigid base layer. When the thickness of GMTL increases from 12 cm to 20 cm, the tensile stress at the bottom of the base layer reduced by about 31%. It is concluded that the increase in modulus of GMTL can significantly reduce the tensile stress at the bottom of the surface layer and increase the shear stress in GMTL, but it has no significant effect on other stresses. e decrease in tension stress at the bottom of the semirigid base layer and increase in the tension stress at the bottom of the surface layer were observed with the increasing thickness of GMTL when the modulus of GMTL is set as 300 MPa. Based on the mechanics calculation results discussed above and the construction requirements in field, it is recommended that the optimum modulus and the thickness of GMTL are 700 MPa and 18 cm, respectively.    Advances in Materials Science and Engineering Table 1 and the FIELD survey on the cumulative equivalent axle of heavy traffic road in the cold region chosen were used to calculate the compressive stress of the GMTL by means of the ABQUES. e results are shown in Table 2.

Determination of Compressive Stress Level. e information in
In this study, the mean value of 0.446 MPa was selected as the permitted compressive stress.

Establishing the Strength Standard
(1) Compressive Strength Standard. When the maximum compressive stress δ max exceeds the permitted value under the effect of vehicle load, permanent deformation will happen in GMTL [22]. Consequently, δ max should be less than the permitted compressive stress. According to the critical conditions, R c can be obtained if δ max is equal to the permitted compressive stress: where K u means the compressive strength coefficient. According to the field investigation of the traffic volume and the "Specifications for Design of highway Asphalt pavement (JTG D50-2017)," the representative of the compressive strength coefficient under different traffic levels in the cold area of Hebei province was calculated. e result is shown in Table 3.
Taking the engineering situation in the field into consideration, the compressive strength coefficient of 2.37 is selected in this study. According to formula (1), the R c required for GMTL is 1.06 MPa under the level of heavy traffic in this area.
(2) Standard of CBR. R c can be turned into the CBR according to the relationship between CBR and R c [23]. In this study, the relationship between unconfined compression strength and CBR is shown in the following formula: According to the previous formula, the CBR standard of GMTL is 354%. e CBR standard can better guide the design and construction of graded macadam materials subjected to the heavy traffic.
(3) Strength Standard Based on the Spatial Attitude Angle of WIAA. In this study, the mass ratio between coarse and fine aggregate is 69 to 31, and the void content is 10.3%. e WIAA was mixed into the aggregates. e heavy compaction test was conducted in one layer with compaction times of 150 under the optimum water content of 5.1%. e spatial attitude angle of WIAA was used to judge the interlocking condition of graded macadam. e calculation method of the spatial attitude angle is shown in the following formula: where Φ is the spatial attitude angle and the unit is degree (°). Φ x is the attitude angle in the x-axis direction. Φ y is the attitude angle in the y-axis direction. Φ z is the attitude angle in the z-axis direction. e strength standard of GMTL based on WIAA is determined according to the relationship between the spatial attitude angle of WIAA and the compaction degree of GMTL (see Figure 12). As presented in Figure 12, with an increase in compaction times, Φ of WIAA showed a steep decreasing trend at the initial stage (less than 75 times), a stable decreasing trend at the middle stage (76∼110 times), and a stable state at the third stage (111∼150 times). is is because the initial stage of compaction is the transition stage of graded macadam from a loose state to a dense state, which causes Φ to decrease sharply [24]. At the middle stage of compaction, the graded macadam was further compacted, and the interlocking skeleton between aggregates was formed at this stage. At this time, the movable space of WIAA is limited, and Φ decreases slowly. At the third stage of compaction, the interlock structure between aggregates in graded macadam had been in a fixed state. At this time, Φ of WIAA is stable at about 0.05 g/cm 3 due to the common drift phenomenon of sensors. When the compaction degree reaches 98% of the specification requirements, the corresponding compaction times are 105, and the spatial attitude angle of WIAA is not in a stable state at this time. erefore, it is inferred that when the compaction degree of the graded macadam meets the requirements, there is still space for further optimization of the interlocking or contact state between the internal aggregates [25]. Taking this experiment as an example, the compaction degree was 99% at the 110 th compaction while Φ of WIAA did not change anymore. erefore, it is inferred that the interlock state between aggregates may be a relatively optimal state in terms of strength and stability. Based on the above analysis, it is concluded that Φ is a better indicator to characterize the strength and stability of GMTL in comparison to compaction degree. According to Φ of WIAA, R c standard, and CBR standard discussed above, the strength control standard of IAP with GMTL is proposed, as shown in the following formula: where Φ N means the stable value of spatial attitude angle of WIAA after N times compaction. e value of N is determined by the actual situation. e three conditions in    Advances in Materials Science and Engineering formula (4) must be reached at the same time. e final optimized pavement construction and parameters are shown in Table 4.

Performance Validation by Pavement-Me Software.
According to the field survey, the main pavement distresses are top-down cracking and bottom-up cracking. e two types of cracking can be calculated using Pavement-Me software with the parameterized input level of Level 2 and Level 3. Pavement structure parameters are mentioned in Table 4. e parameter of material is expressed by dynamic modulus. e traffic parameter is the heavy traffic grade. e climate data can be obtained from the field survey and the meteorological data. e research in this part is designed to conduct a performance comparison. Hence, the default value is used for the correction factor of the MEPDG method [26]. e specific parameter is shown in Table 5. e calculation results of Pavement-Me are shown in Figure 13.
From Figure 13, the top-down cracking of optimized pavement has been reduced by about 29.3% for the 20 years' service. For the bottom-up cracking, the bottom-up cracking of optimized pavement has been reduced by about 32.6% [27]. It is concluded that the asphalt pavement structure with GMTL has good resistance to cracking, which is consistent with the previous studies [28]. ese findings can guide the construction and design of IAP in cold areas.

Conclusion
(1) With the increase in modulus of GMTL, the deformation in the surface layer would get less under a certain load, which makes the tension stress decreased. However, the force direction of the O point chosen in this study had a trend to horizon direction from the vertical direction as long as the modulus of GMTL reached or closed to that of the asphalt mixture layer. e tensile stress at the bottom of the surface layer reduced up to 58% and the shear stress in GMTL increased up to 17% when the modulus of GMTL increases from 300 MPa to 800 MPa. e change in modulus has no significant influence on the maximum shear stress in the asphalt surface layer and the tensile stress in the base layer bottom.
(2) When the thickness of GMTL increases from 12 cm to 20 cm, the tensile stress in the bottom of the base layer reduced by about 31%. Combining the mechanical calculation results with the field technical requirements, the recommended optimal parameters of GMTL are the modulus of 700 MPa and the thickness of 18 cm. (3) e spatial attitude angle Φ N of wireless intelligent attitude aggregate (WIAA), the compressive strength R c standard, and the CBR standard were analyzed, and the strength control standard of inverted asphalt pavement with GMTL was proposed, that is, CBR ≥ 354%, R c ≥ 1.06 MPa, and Φ N ≤ 3°. (4) In the cold region of Hebei, China, the optimized inverted asphalt pavement structure has a significant improvement in crack resistance. Taking the 20-year service life as an example, the damage degree of topdown cracks reduced by 29.3% and that of the bottom-up cracks reduced by 32.6% in comparison to the original structure.
Data Availability e data presented in this study are available on request from the corresponding author. e data are not publicly available due to privacy.

Conflicts of Interest
e authors declare no conflicts of interest.