Optimization of Pavement Structure Using High-Modulus Asphalt Coating Considering the Effects of Base-Course Combinations

Abstract

High-modulus asphalt concrete (HMAC) has been widely used in the surface coating of high-grade pavement. Due to HMAC’s modulus being significantly higher than traditional asphalt concrete, the mechanical responses of a pavement structure using an HMAC coating must be notably different from those of a traditional asphalt pavement structure. Moreover, when asphalt surface coating is fixed, the selection of base-course combinations will determine the mechanical response of the whole pavement structure. However, previous studies usually analyzed the mechanical response of pavement structures at limited combinations of base-courses, resulting in difficulties comprehensively understanding the laws of mechanics and effectively optimizing the HMAC pavement structure. Hence, in this study, a total of 108 groups of numerical experiments under six working conditions of base-course combinations are carried out using orthogonal experimental design to investigate the mechanical response of pavement structures using HMAC coatings using the PR MODULE high-modulus additive. The effects of pavement thickness, material modulus, and structural combination on mechanical responses are analyzed for the 108 groups to determine the optimal pavement combinations based on the balance of mechanical response and economic efficiency. The results show the following: The effect of the base layer type on mechanical response is more significant than that of the subbase layer type. Surface and undersurface layer thickness for the granular material base layer; surface and base layer thickness for the asphalt mixture base layer; and base layer thickness, subbase layer modulus, and base layer modulus for the inorganic binder mixture base layer are the key factors for mechanical response. Finally, six recommended HMAC pavement structure configurations for various base-courses are proposed.

1. Introduction

Owing to the rapid increase in traffic channelization in recent years, pavement rutting has become one of the most serious asphalt pavement damages in China, especially in high-temperature regions [1]. In response to this issue, modified asphalt binders and concrete have been extensively utilized in asphalt pavements [2]. Based on a limited review, various modifiers, such as styrene–butadiene–styrene (SBS) [3], rubber [4], and polyethylene (PE) [5], have been employed to enhance the rutting resistance of asphalt pavement. However, existing modifiers struggle to strike a balance between performance, cost-effectiveness, and technological complexity [6]. Due to its exceptional performance and well-established production technology, high-modulus asphalt binder and concrete have garnered increased attention and are being increasingly adopted in high-grade pavements [7].

Previous studies have confirmed significant differences in the performance of high-modulus asphalt concrete (HMAC) compared to traditional asphalt concrete [8]. Evidently, the mechanical responses of pavement structures using HMAC coatings also vary from those of traditional asphalt pavement [9]. Furthermore, due to the distinct characteristics of different asphalt-based materials, selecting an appropriate pavement combination is essential for ensuring pavement performance [10]. Norouzi et al. [11] examined common pavement design parameters by assessing the performance of asphalt pavement for the Korea Road Corporation. Their findings revealed that the thickness, modulus, and material type of the pavement structure course significantly impact fatigue and rutting resistance. Lv et al. [12] discovered that early damage to asphalt pavement with a semi-rigid base-course was attributed to the improper matching of pavement structural moduli. They evaluated three typical pavement structures to determine the influence of pavement structure on pavement service life. Shirzad et al. [13] investigated three different pavement structures under varying traffic levels and climatic zones. Pan et al. [14] integrated the two-mode elastic theory into pavement mechanics analysis. Jiang et al. [15] developed a numerical model of flexible base asphalt pavement under uneven tire vertical contact pressure using the three-dimensional software EverStressFE (version 1.0) to study the distribution of non-uniformity and uniformity deformation, as well as the mechanical response of asphalt pavement. Li et al. [16] employed the three-dimensional finite element method to conduct dynamic simulation analysis of typical asphalt pavement structures. Liu et al. [17] explored the mechanical response of four types of asphalt pavement with different base-courses: cement-treated base, cement-treated base + graded gravel base, asphalt-treated base + cement-treated base, and asphalt-treated base + graded gravel base. Rys et al. [18] introduced a method to consider dynamic loads in the axle load spectrum for empirical pavement design and highlighted the impact of the dynamic axial load spectrum on pavement performance. Assobga et al. [19] analyzed the distribution of mechanical parameters in three types of semi-rigid pavement structures. Zeiada et al. [20] investigated the influence of pavement design factors on mechanical response in warm regions and compared it to that of factors previously identified in cold regions. They proved that there was a significant difference in mechanical response when selecting different pavement combinations.

On one hand, due to HMAC’s modulus being significantly higher than traditional asphalt concrete, the mechanical responses of a pavement structure using an HMAC coating must be notably different from those of a traditional asphalt pavement structure. On the other hand, obviously, when asphalt surface coatings are fixed, the selection of a base-course will determine the mechanical response of the whole pavement structure. However, previous studies usually analyzed the mechanical response of pavement structures at limited combinations of base-courses. It was hard to comprehensively understand the laws of mechanics of and effectively optimize the pavement structure. The lack of previous studies will also impact the application of HMAC in pavement structures, which could result in performance deficiencies and economic waste.

Hence, in this study, a total of 108 groups of numerical experiments under six working conditions of base-course combinations are carried out using orthogonal experimental design to investigate the mechanical response of pavement structures using HMAC coatings using the PR MODULE high-modulus additive. The effects of pavement thickness, material modulus, and pavement combination on the mechanical responses are analyzed for the 108 groups to determine the optimal pavement combinations under different working conditions based on the balance of mechanical response and economic efficiency.

2. Calculation Model

2.1. Pavement Mechanical Index

The numerical model and the calculated point are shown in Figure 1. In the XOY horizontal plane of Figure 1, point A’s coordinates are (0 cm, −15.975 cm), point B’s coordinates are (0 cm, −5.325 cm), point C’s coordinates are (0 cm, 0 cm), and point D’s coordinates are (0 cm, −2.6625 cm). The position coordinates of the four points are determined according to the Chinese design specification “Specifications for Design of Highway Asphalt Pavement (JTG D50-2017)”. The values of mechanical response are selected by the maximum values of points A, B, C, and D for each mechanical response. The maximum values represent the worst case of one mechanical response. The equivalent circle has a radius of δ = 10.65 cm, and the standard axial load condition of p = 0.707 MPa is utilized.

The current pavement design code classifies pavement structures into six types based on their base and base materials (asphalt mixture, inorganic binder stability materials, and granular materials) [21]. The design index system is depicted in Figure 2.

Table 1. Mechanical response and vertical position corresponding to each design index.

Design Index	Mechanical Response	Vertical Position
Tensile strain of asphalt mixture layer bottom	Horizontal tensile strain along running direction	Asphalt mixture layer bottom
Tensile stress of inorganic binder-stabilized material layer bottom	Horizontal tensile stress along the driving direction	Inorganic binder-stabilized material layer bottom
Permanent deformation of asphalt mixture layer	Vertical compressive stress	Top surface of each layer of asphalt mixture layer
Vertical compressive strain at the top of subgrade	Vertical compressive strain	Subgrade top

presents the corresponding mechanical response and vertical position of each design index. It should be noted that the HMAC is primarily adopted in the surface layer and has a strong rutting resistance. Therefore, the permanent deformation of the surface layer is not investigated in the pavement calculation model.

Based on Figure 2 and Table 1, six HMAC pavement structures are established with different bases and subbases, as shown in

Table 2. HMAC pavement structures.

Working Condition	Surface Layer	Undersurface Layer	Base Layer	Subbase Layer
No. 1	HMAC	AC-25 asphalt mixture	Cement-stabilized macadam	Cement-stabilized macadam
No. 2			Cement-stabilized macadam	Graded broken stone
No. 3			Asphalt-treated base	Graded broken stone
No. 4			Asphalt-treated base	Cement-stabilized macadam
No. 5			Graded broken stone	Cement-stabilized macadam
No. 6			Graded broken stone	Graded broken stone

.

2.2. HMAC Parameters

In compliance with the current pavement design code, the HMAC’s parameters when used as surface layer are chosen based on the dynamic compression modulus at 20 °C and 10 Hz. The test results of the dynamic modulus of the HMAC are presented in

Table 3. Dynamic modulus results of the HMAC.

Frequency (Hz)	0.1	0.5	1	5	10	25
Modulus (MPa)	8700	12,226	13,667	15,731	16,791	18,868

. In this study, the PR MODULE high-modulus additive is adopted to prepare the HMAC, of which the technical parameters are listed in

Table 4. Technical parameters of PR MODULE high-modulus additive.

Tensile Strength (MPa)	Elongation at Break (%)	Density (g·cm−3)	Melt Flow Rate (g/10 min)	Rockwell Hardness	Vicat Softening Point (°C)	Resin Content (%)	Particle Diameter (mm)
18	28	0.94	1.6	62	126	69	4

.

Based on the dynamic modulus test results presented in Table 2, a parameter of 16,791 MPa is used for the HMAC in the pavement mechanical calculations for the subsequent pavement structure analysis in this paper.

2.3. Verification

In order to verify the feasibility of the numerical experiments shown in Section 2.1, six large-scale pavement structure samples (see Figure 3) are prepared according to the structural combinations presented in Table 2. Strain sensors are embedded between different layers in the samples to record the mechanical response (see Table 1) of the pavement structures under the action of a standard wheel load (0.707 MPa). The errors of the stress and strain between the measured results and calculated results are presented in

Table 5. Comparison between measured results and calculated results.

Working Condition	Design Index	Layer	Test Value	Simulation Value	Error (%)
No. 1	Tensile stress of layer bottom (×10−4 MPa)	Subbase layer	1069	976	8.7
		Base layer	1480	1567	5.9
	Permanent deformation (×10−4 MPa)	Undersurface layer	7099	6453	9.1
No. 2	Tensile stress of layer bottom (×10−4 MPa)	Base layer	3212	2926	8.9
	Permanent deformation (×10−4 MPa)	Undersurface layer	5482	6101	11.3
No. 3	Permanent deformation (×10−4 MPa)	Undersurface layer	5986	6399	6.9
		Base layer	3144	3370	7.2
	Vertical compressive strain (με)	Subgrade	19.0	20.7	8.9
	Tensile strain of layer bottom (με)	Surface layer	29.2	30.8	5.3
		Undersurface layer	60.9	58.1	4.6
		Base layer	46.0	49.4	7.3
No. 4	Tensile stress of layer bottom (×10−4 MPa)	Subbase layer	2346	2463	5.0
	Permanent deformation (×10−4 MPa)	Undersurface layer	7636	6590	13.7
		Base layer	3937	4414	12.1
No. 5	Tensile stress of layer bottom (×10−4 MPa)	Subbase layer	2733	3003	9.9
	Permanent deformation (×10−4 MPa)	Undersurface layer	6178	5443	11.9
	Tensile strain of layer bottom (με)	Surface layer	22.1	19.9	9.8
		Undersurface layer	57.7	63.9	10.7
No. 6	Tensile strain of layer bottom (με)	Surface layer	20.0	21.9	9.7
		Undersurface layer	84.4	77.1	8.6
	Vertical compressive strain (με)	Subgrade	270	286	6.1
	Permanent deformation (×10−4 MPa)	Undersurface layer	5788	5371	7.2

.

As shown in Table 5, the errors between the measured results and calculated results are all less than 14 %, proving the feasibility of the numerical experiments.

2.4. Pavement Structure Model

Due to the numerous possible combinations of pavement structures, this study employed the orthogonal test method to analyze the HMAC pavement structure and obtain scientifically valid calculation results. By varying the thickness and modulus of different layers, the influence of the pavement structure and material parameters on pavement mechanical response (refer to Table 1) was investigated under each working condition. The key mechanical control index was proposed for each working condition. Based on the principle of optimal mechanical response and economy, a recommended HMAC pavement combination form was proposed to serve as a basis for the pavement’s structural design.

The orthogonal test designs for various working conditions are presented in

Table 6. Orthogonal test design for working condition No. 1.

No.	Surface Layer		Undersurface Layer		Base Layer		Subbase Layer		Soil Matrix
	Thickness (cm)	Modulus (MPa)	Thickness (cm)	Modulus (MPa)	Thickness (cm)	Modulus (MPa)	Thickness (cm)	Modulus (MPa)	Modulus (MPa)
1-1	3	16,791	5	10,000	30	9000	15	7000	50
1-2	3		7	11,500	36	11,500	18	8500	50
1-3	3		9	13,000	40	14,000	20	10,000	50
1-4	4		5	10,000	36	11,500	20	10,000	50
1-5	4		7	11,500	40	14,000	15	7000	50
1-6	4		9	13,000	30	9000	18	8500	50
1-7	5		5	11,500	30	14,000	18	10,000	50
1-8	5		7	13,000	36	9000	20	7000	50
1-9	5		9	10,000	40	11,500	15	8500	50
1-10	3		5	13,000	40	11,500	18	7000	50
1-11	3		7	10,000	30	14,000	20	8500	50
1-12	3		9	11,500	36	9000	15	10,000	50
1-13	4		5	11,500	40	9000	20	8500	50
1-14	4		7	13,000	30	11,500	15	10,000	50
1-15	4		9	10,000	36	14,000	18	7000	50
1-16	5		5	13,000	36	14,000	15	8500	50
1-17	5		7	10,000	40	9000	18	10,000	50
1-18	5		9	11,500	30	11,500	20	7000	50

,

Table 7. Orthogonal test design for working condition No. 2.

No.	Surface Layer		Undersurface Layer		Base Layer		Subbase Layer		Soil Matrix
	Thickness (cm)	Modulus (MPa)	Thickness (cm)	Modulus (MPa)	Thickness (cm)	Modulus (MPa)	Thickness (cm)	Modulus (MPa)	Modulus (MPa)
2-1	3	16,791	5	10,000	30	9000	15	200	50
2-2	3		7	11,500	36	11,500	18	320	50
2-3	3		9	13,000	40	14,000	20	440	50
2-4	4		5	10,000	36	11,500	20	440	50
2-5	4		7	11,500	40	14,000	15	200	50
2-6	4		9	13,000	30	9000	18	320	50
2-7	5		5	11,500	30	14,000	18	440	50
2-8	5		7	13,000	36	9000	20	200	50
2-9	5		9	10,000	40	11,500	15	320	50
2-10	3		5	13,000	40	11,500	18	200	50
2-11	3		7	10,000	30	14,000	20	320	50
2-12	3		9	11,500	36	9000	15	440	50
2-13	4		5	11,500	40	9000	20	320	50
2-14	4		7	13,000	30	11,500	15	440	50
2-15	4		9	10,000	36	14,000	18	200	50
2-16	5		5	13,000	36	14,000	15	320	50
2-17	5		7	10,000	40	9000	18	440	50
2-18	5		9	11,500	30	11,500	20	200	50

,

Table 8. Orthogonal test design for working condition No. 3.

No.	Surface Layer		Undersurface Layer		Base Layer		Subbase Layer		Soil Matrix
	Thickness (cm)	Modulus (MPa)	Thickness (cm)	Modulus (MPa)	Thickness (cm)	Modulus (MPa)	Thickness (cm)	Modulus (MPa)	Thickness (cm)
3-1	3	16,791	5	10,000	10	7000	20	200	50
3-2	3		7	11,500	15	9000	25	320	50
3-3	3		9	13,000	20	11,000	30	440	50
3-4	4		5	10,000	15	9000	30	440	50
3-5	4		7	11,500	20	11,000	20	200	50
3-6	4		9	13,000	10	7000	25	320	50
3-7	5		5	11,500	10	11,000	25	440	50
3-8	5		7	13,000	15	7000	30	200	50
3-9	5		9	10,000	20	9000	20	320	50
3-10	3		5	13,000	20	9000	25	200	50
3-11	3		7	10,000	10	11,000	30	320	50
3-12	3		9	11,500	15	7000	20	440	50
3-13	4		5	11,500	20	7000	30	320	50
3-14	4		7	13,000	10	9000	20	440	50
3-15	4		9	10,000	15	11,000	25	200	50
3-16	5		5	13,000	15	11,000	20	320	50
3-17	5		7	10,000	20	7000	25	440	50
3-18	5		9	11,500	10	9000	30	200	50

,

Table 9. Orthogonal test design for working condition No. 4.

No.	Surface Layer		Undersurface Layer		Base Layer		Subbase Layer		Soil Matrix
	Thickness (cm)	Modulus (MPa)	Thickness (cm)	Modulus (MPa)	Thickness (cm)	Modulus (MPa)	Thickness (cm)	Modulus (MPa)	Thickness (cm)
4-1	3	16,791	5	10,000	10	7000	20	7000	50
4-2	3		7	11,500	15	9000	25	8500	50
4-3	3		9	13,000	20	11,000	30	10,000	50
4-4	4		5	10,000	15	9000	30	10,000	50
4-5	4		7	11,500	20	11,000	20	7000	50
4-6	4		9	13,000	10	7000	25	8500	50
4-7	5		5	11,500	10	11,000	25	10,000	50
4-8	5		7	13,000	15	7000	30	7000	50
4-9	5		9	10,000	20	9000	20	8500	50
4-10	3		5	13,000	20	9000	25	7000	50
4-11	3		7	10,000	10	11,000	30	8500	50
4-12	3		9	11,500	15	7000	20	10,000	50
4-13	4		5	11,500	20	7000	30	8500	50
4-14	4		7	13,000	10	9000	20	10,000	50
4-15	4		9	10,000	15	11,000	25	7000	50
4-16	5		5	13,000	15	11,000	20	8500	50
4-17	5		7	10,000	20	7000	25	10,000	50
4-18	5		9	11,500	10	9000	30	7000	50

,

Table 10. Orthogonal test design for working condition No. 5.

No.	Surface Layer		Undersurface Layer		Base Layer		Subbase Layer		Soil Matrix
	Thickness (cm)	Modulus (MPa)	Thickness (cm)	Modulus (MPa)	Thickness (cm)	Modulus(MPa)	Thickness (cm)	Modulus (MPa)	Thickness (cm)
5-1	3	16,791	5	10,000	30	300	15	7000	50
5-2	3		7	11,500	36	500	18	8500	50
5-3	3		9	13,000	40	700	20	10,000	50
5-4	4		5	10,000	36	500	20	10,000	50
5-5	4		7	11,500	40	700	15	7000	50
5-6	4		9	13,000	30	300	18	8500	50
5-7	5		5	11,500	30	700	18	10,000	50
5-8	5		7	13,000	36	300	20	7000	50
5-9	5		9	10,000	40	500	15	8500	50
5-10	3		5	13,000	40	500	18	7000	50
5-11	3		7	10,000	30	700	20	8500	50
5-12	3		9	11,500	36	300	15	10,000	50
5-13	4		5	11,500	40	300	20	8500	50
5-14	4		7	13,000	30	500	15	10,000	50
5-15	4		9	10,000	36	700	18	7000	50
5-16	5		5	13,000	36	700	15	8500	50
5-17	5		7	10,000	40	300	18	10,000	50
5-18	5		9	11,500	30	500	20	7000	50

and

Table 11. Orthogonal test design for working condition No. 6.

No.	Surface Layer		Undersurface Layer		Base Layer		Subbase Layer		Soil Matrix
	Thickness (cm)	Modulus (MPa)	Thickness (cm)	Modulus (MPa)	Thickness (cm)	Modulus (MPa)	Thickness (cm)	Modulus (MPa)	Thickness (cm)
6-1	3	16,791	5	10,000	30	300	15	200	50
6-2	3		7	11,500	36	500	18	320	50
6-3	3		9	13,000	40	700	20	440	50
6-4	4		5	10,000	36	500	20	440	50
6-5	4		7	11,500	40	700	15	200	50
6-6	4		9	13,000	30	300	18	320	50
6-7	5		5	11,500	30	700	18	440	50
6-8	5		7	13,000	36	300	20	200	50
6-9	5		9	10,000	40	500	15	320	50
6-10	3		5	13,000	40	500	18	200	50
6-11	3		7	10,000	30	700	20	320	50
6-12	3		9	11,500	36	300	15	440	50
6-13	4		5	11,500	40	300	20	320	50
6-14	4		7	13,000	30	500	15	440	50
6-15	4		9	10,000	36	700	18	200	50
6-16	5		5	13,000	36	700	15	320	50
6-17	5		7	10,000	40	300	18	440	50
6-18	5		9	11,500	30	500	20	200	50

(please refer to the subsequent Section).

3. Mechanical Responses

Table 12. Laws of ranges.

Working Condition	Index	Range
		Thickness of Surface Layer	Thickness of Undersurface Layer	Modulus of Undersurface Layer	Thickness of Base Layer	Modulus of Base Layer	Thickness of Subbase Layer	Modulus of Subbase Layer
No. 1	Tensile stress of cement-stabilized macadam subbase layer bottom	118	173	27	449	154	203	407
	Tensile stress of cement-stabilized macadam base layer bottom	180	114	5	120	411	270	279
	Permanent deformation of asphalt mixture undersurface layer	914	662	654	675	572	611	675
No. 2	Tensile stress of cement-stabilized macadam subbase layer bottom	220	377	89	968	435	55	105
	Permanent deformation of asphalt mixture undersurface layer	1382	334	32	210	166	192	73
No. 3	Tensile strain of surface layer bottom	12.1	1.7	4.9	4.3	1.7	1.2	2.4
	Tensile strain of asphalt mixture undersurface layer bottom	90	51	41	159	37	93	46
	Tensile strain of asphalt mixture base layer bottom	13.6	11.8	3.5	23.7	3.5	9.6	4.8
	Permanent deformation of asphalt mixture undersurface layer	746	55	46	167	91	66	64
	Permanent deformation of asphalt mixture base layer	567	1020	313	521	464	281	221
	Vertical compressive strain at top of subgrade	3.2	5.5	1.3	11.4	2.3	2.3	0.9
No. 4	Tensile stress of cement-stabilized macadam subbase layer bottom	201	396	101	664	201	664	357
	Permanent deformation of asphalt mixture undersurface layer	634	322	11	27	134	22	9
	Permanent deformation of asphalt mixture base layer	861	1131	331	150	134	1505	172
No. 5	Tensile stress of cement-stabilized macadam subbase layer bottom	668	320	332	317	697	317	529
	Permanent deformation of asphalt mixture undersurface layer	855	747	53	196	329	163	105
	Tensile strain of asphalt mixture surface layer bottom	5.9	5.1	2.5	1.6	1.1	1.7	0.4
	Tensile strain of asphalt mixture undersurface layer bottom	18.4	16.4	11.3	6.4	29.0	8.0	8.7
No. 6	Permanent deformation of asphalt mixture undersurface layer	1003	890	51	47	234	35	45
	Vertical compressive strain at the top of subgrade	371	668	294	570	548	483	382
	Tensile strain of asphalt mixture surface layer bottom	8.2	6.4	2.3	2.3	0.6	1.5	0.2
	Tensile strain of asphalt mixture undersurface layer bottom	12.2	22.9	1.1	4.5	3.1	24.3	5.6

shows the laws of the ranges for each influence factor under the six working conditions.

3.1. Condition No. 1 (HMAC Surface Layer + Asphalt Concrete Undersurface Layer + Inorganic Binder Base Layer + Inorganic Binder Subbase Layer)

According to Table 12, the difference in range between the thickness and modulus of the inorganic binder base is significantly larger than that of other structural and material parameters, indicating their greater impact on the tensile stress of the inorganic binder base. Figure 4 displays the influential trends in the key indices in working condition No. 1 on the tensile stress at the bottom of the subbase layer. Figure 4 displays the influential trends in the key indices in working condition No. 1 on the tensile stress at the bottom of the subbase layer.

Figure 4 illustrates that an increase in the thickness of the inorganic binder base and a decrease in the modulus of the inorganic binder base lead to a decreasing trend in the tensile stress at the bottom of the subbase layer. Therefore, the thickness of the inorganic binder base is considered high, while the modulus of the inorganic binder base is considered low.

Table 12 illustrates that the modulus, thickness, and modulus of the inorganic binder base have a significantly greater range difference than other structural layer parameters, indicating their significant influence on the tensile stress of the inorganic binder base. Figure 5 illustrates the trends in the key indicators on the tensile stress of the base layer.

Figure 5 illustrates that as the modulus of the inorganic binder base increases and the thickness of the inorganic binder base decreases, the tensile stress of the inorganic binder base tends to increase. Therefore, it is advisable to have a low modulus and thickness of the inorganic binder base, while a high thickness of the inorganic binder base is recommended.

Table 12 shows that the thickness of the surface layer, the thickness and modulus of the undersurface layer, the thickness of the base layer, and the modulus of the base layer all significantly affect the permanent deformation of the undersurface layer in the asphalt mixture, with the thickness of the HMAC surface layer having the most significant impact. Figure 6 depicts the influential trends in the key indicators on the permanent deformation of the undersurface layer.

As illustrated in Figure 6, each key parameter demonstrates a distinct peak or inflection point. Therefore, to adhere to the principle of minimizing permanent deformation in the undersurface layer of the asphalt mixture, it is recommended to use a 4 cm HMAC pavement surface layer, a 7 cm undersurface layer, a 36 cm inorganic binder base layer, and an 18 cm inorganic binder subbase layer, with a low modulus for each structural layer.

To summarize, based on the economic analysis, the recommended HMAC pavement structure for working condition No. 1 includes a 4 cm HMAC surface layer, a 7 cm asphalt mixture undersurface layer, a 40 cm inorganic binder base, and an 18 cm inorganic binder subbase, each with a low modulus for optimal performance.

3.2. Condition No. 2 (HMAC Surface Layer + Asphalt Concrete Undersurface Layer + Inorganic Binder Base Layer + Granular Base Subbase)

Table 12 shows that the thickness of the inorganic binder base layer significantly impacts the tensile stress at its bottom, while the thickness of the HMAC surface layer influences the permanent deformation of the undersurface layer. Additionally, the modulus of the inorganic binder base and the thickness of the granular base also play a role in each index. Therefore, it is crucial to pay close attention to the thickness of the HMAC surface layer, the thickness and modulus of the inorganic binder base, and the thickness of the granular base.

Figure 7 and Figure 8 illustrate the influential trends in the aforementioned key indicators on the tensile stress at the bottom of the inorganic binder base layer and the permanent deformation of the undersurface layer, respectively.

Based on these influential trends in the key indicators and comprehensive economic considerations, the recommended HMAC pavement structure for working condition No. 2 includes a 5 cm HMAC surface layer, a 5 cm asphalt concrete undersurface layer, a 36 cm inorganic binder base, and a 15 cm granular subbase. A low modulus is suggested for the inorganic binder base, while the modulus of the granular subbase and asphalt concrete undersurface layer can be flexibly selected based on the actual project requirements.

3.3. Condition No. 3 (HMAC Surface Layer + Asphalt Concrete Undersurface Layer + Asphalt Mixture Base Layer + Granular Subbase Layer)

According to Table 12, the thickness of the HMAC surface layer significantly impacts the tensile strain at the bottom of the surface layer, the permanent deformation at the bottom of the asphalt concrete layer, and the tensile strain at the bottom of the asphalt concrete layer. The thickness of the asphalt mixture base layer significantly affects the permanent deformation of the asphalt mixture base layer, and the modulus of the asphalt mixture base layer has a significant impact on the tensile strain at the bottom of the HMAC surface layer. Additionally, the thickness of the asphalt mixture base layer significantly influences the vertical compressive strain at the top surface of the HMAC surface layer and the tensile strain of the asphalt mixture base layer. Therefore, careful attention should be given to the thickness of the HMAC surface layer, the thickness and modulus of the undersurface layer, and the thickness of the asphalt mixture base layer.

Figure 9, Figure 10, Figure 11, Figure 12, Figure 13 and Figure 14 illustrate the influential trends in the key indicators on the permanent deformation of the undersurface layer, the permanent deformation of the asphalt mixture base layer, the vertical compressive strain at the top surface of the roadbed, and the tensile strain at the surface layer, undersurface layer, and asphalt mixture base layer, respectively.

Based on the development trends corresponding to each key index in the range charts and comprehensive economic considerations, the recommended HMAC pavement structure for working condition No. 3 includes a 4 cm HMAC surface layer, a 9 cm asphalt concrete undersurface layer, a 20 cm asphalt mixture base layer, and a 20 cm granular subbase layer. A medium to high modulus is recommended for the undersurface layer, while the modulus of the granular subbase and asphalt mixture base layer can be flexibly selected based on the actual project requirements.

3.4. Condition No. 4 (HMAC Surface Layer + Asphalt Concrete Undersurface Layer + Asphalt Mixture Base Layer + Inorganic Binder Subbase Layer)

According to Table 12, the thickness of the HMAC surface layer and the undersurface layer significantly impact the permanent deformation of the undersurface layer and the asphalt mixture base layer. Additionally, the thickness of the inorganic binder base has a significant influence on the tensile stress at the bottom of the base layer and the permanent deformation of the asphalt mixture base layer. The thickness of the asphalt mixture base layer also noticeably impacts the tensile stress of the inorganic binder base layer. Therefore, careful attention should be given to the thickness of the HMAC surface layer, the undersurface layer, the asphalt mixture base layer, and the inorganic binder base layer when designing the pavement structure for working condition No. 4.

Figure 15, Figure 16 and Figure 17 illustrate influential trends in the key indicators on tensile stress at the bottom of the subbase layer, the permanent deformation of the undersurface layer, and the permanent deformation of the asphalt mixture base layer under working condition No. 4.

Based on the development trends corresponding to each key index in the range chart and comprehensive economic considerations, the recommended HMAC pavement structure for working condition No. 4 includes a 5 cm HMAC surface layer, a 7 cm asphalt concrete undersurface layer, a 20 cm asphalt mixture base layer, and a 25 cm inorganic binder base layer. The modulus of the subbase layer and base layer should be as low as possible, while the modulus of the undersurface layer and base layer can be flexibly selected based on the actual situation.

3.5. Condition No. 5 (HMAC Surface Layer + Asphalt Concrete Undersurface Layer + Granular Base Layer + Inorganic Binder Subbase Layer)

According to Table 12, the thicknesses of the HMAC surface layer and the undersurface layer of asphalt concrete have a significant impact on the tensile strain at the bottom of the subbase layer and the permanent deformation of the undersurface layer. Moreover, the thickness of the HMAC surface layer, the modulus of the granular undersurface layer, and the modulus of the inorganic binder base play a crucial role in the tensile stress at the bottom of the subbase layer. The thickness of the HMAC surface layer also notably affects the tensile stress at the bottom of the asphalt concrete undersurface layer. Therefore, it is essential to carefully consider the thickness of the HMAC surface layer, the undersurface layer, the modulus of the granular base layer, and the modulus of the inorganic binder subbase when designing the pavement structure for working condition No. 5.

Figure 18, Figure 19, Figure 20 and Figure 21 illustrate the trends in the key indicators that affect the bottom tensile stress of the subbase layer, the permanent deformation of the undersurface layer, the tensile strain of the bottom of the surface layer, and the tensile strain of the base layer under working condition No. 5.

Based on the development trends corresponding to each key index in the range chart and a comprehensive consideration of the economy, the recommended HMAC pavement structure for working condition No. 5 is as follows: a 5 cm HMAC surface layer, a 5 cm asphalt concrete undersurface layer, a 30 cm granular base layer, and a 15 cm inorganic binder subbase layer. It is advisable for the modulus of the granular base layer to be as high as possible, while the modulus of the inorganic binder subbase layer should be as low as possible. The modulus of the asphalt concrete undersurface layer can be chosen flexibly based on the actual project requirements.

3.6. Condition No. 6 (HMAC Surface Layer + Asphalt Concrete Undersurface Layer + Granular Base Layer + Inorganic Binder Base Layer)

According to Table 12, the thicknesses of the HMAC surface layer and the undersurface layer of asphalt concrete significantly affect the tensile strain of the surface layer and the permanent deformation of the undersurface layer. Moreover, the thickness of the undersurface layer of asphalt concrete and the modulus of the granular subbase has a significant impact on the tensile strain at the bottom of the undersurface layer. The thickness of the asphalt concrete undersurface layer, the thickness and modulus of the granular subbase, and the thickness of the subbase layer have notable effects on the vertical compressive strain at the top surface of the subgrade. Therefore, it is crucial to consider the thickness of the HMAC surface layer, the thickness of the undersurface layer of asphalt concrete, the thickness and modulus of the granular base, and the thickness of the subbase layer when designing the pavement structure for various working conditions.

Figure 22, Figure 23, Figure 24 and Figure 25 depict the trends in the key indices that affect the bottom strain of the surface layer, bottom strain of the undersurface layer, vertical compressive strain of the top surface of the subgrade, and permanent deformation of the undersurface layer under working condition No. 6.

Based on the development trends corresponding to each key index in the range chart and a comprehensive consideration of the economy, the recommended HMAC pavement structure for working condition No. 6 is as follows: a 4 cm HMAC surface layer, a 7 cm asphalt concrete undersurface layer, a 36 cm granular base layer, and a 15 cm granular subbase layer. It is advisable for the modulus of the granular base layer to be as high as possible. The moduli of the asphalt concrete undersurface layer and the granular subbase layer can be flexibly selected based on the actual project requirements.

4. Discussion

According to the analysis and discussion in Section 3, the key control indices of HMAC pavement mechanical response under different working conditions are shown in

Table 13. Control index influence degree.

Working Condition	Design Index		Surface Layer Thickness	Undersurface Layer Thickness	Undersurface Layer Modulus	Base layer Thickness	Base Layer Modulus	Subbase Layer Thickness	Subbase Layer Modulus
No. 1	Tensile stress of inorganic binder mixture layer bottom	Subbase layer				✔			✔
		Base layer					✔	✔	✔
	Permanent deformation of asphalt mixture layer	Undersurface layer	✔	✔	✔	✔	✔	✔	✔
No. 2	Tensile stress of inorganic binder mixture layer bottom	Base layer				✔	✔
	Permanent deformation of asphalt concrete layer	Undersurface layer	✔
No. 3	Permanent deformation of asphalt concrete layer	Undersurface layer	✔
		Base layer	✔	✔		✔	✔
	Vertical compressive strain at top surface	Subgrade				✔
	Tensile strain of asphalt mixture layer bottom	Surface layer	✔
		Undersurface layer	✔			✔		✔
		Base layer				✔
No. 4	Tensile stress of inorganic binder mixture layer bottom	Subbase layer				✔		✔
	Permanent deformation of asphalt mixture layer	Undersurface layer	✔
		Base layer	✔	✔				✔
No. 5	Tensile stress of inorganic binder mixture layer bottom	Subbase layer	✔				✔		✔
	Permanent deformation of asphalt mixture layer	Undersurface layer	✔
	Tensile strain of asphalt mixture layer bottom	Surface layer	✔	✔
		Undersurface layer					✔
No. 6	Tensile strain of asphalt mixture layer bottom	Surface layer	✔	✔
		Undersurface layer		✔				✔
	Vertical compressive strain at top surface	Subgrade		✔		✔	✔	✔
	Permanent deformation of asphalt mixture layer	Undersurface layer	✔	✔

. In Table 3, “✔” represents the key factor for one design index.

The recommended pavement structures for the six different working conditions are presented in

Table 14. Recommended pavement structures.

Working Condition	Surface Layer Thickness (cm)	Undersurface Layer Thickness (cm)	Undersurface Layer Modulus (MPa)	Base Layer Thickness (cm)	Base Layer Modulus (MPa)	Subbase Layer Thickness (cm)	Subbase Layer Modulus (MPa)
No. 1	4	7	Low value	40	Low value	18	Low value
No. 2	5	5	Flexible	40	Low value	15	Flexible
No. 3	4	9	Medium value	20	Flexible	20	Flexible
No. 4	5	7	Flexible	20	Flexible	25	Low value
No. 5	5	5	Flexible	30	High value	15	Low value
No. 6	4	7	Flexible	36	High value	15	Flexible

.

5. Conclusions

In this study, a total of 108 groups of numerical experiments under six working conditions were conducted using orthogonal experimental design. The mechanical response of HMAC pavement structure under different working conditions was analyzed. Finally, the optimal pavement combinations under different working conditions were determined based on the balance of mechanical response and economic efficiency. The main conclusions are as follows:

• The influences of pavement thickness and material modulus on the mechanical response of HMAC pavement under different combinations of base and subbase layer are revealed. The effect of base layer type on mechanical response is more significant than that of subbase layer type.
• Based on mechanical response laws, key control indices that affect the mechanical response of HMAC pavement under various base and subbase layer combinations are proposed.
• For a granular material base layer, surface and undersurface layer thickness are the key factors for mechanical response. A thick surface layer and thin undersurface layer are beneficial for the mechanical response of pavement structure.
• For an asphalt mixture base layer, surface and base layer thickness are the key factors for mechanical response. A thick surface layer and base layer provide a low mechanical response in the pavement structure.
• For an inorganic binder mixture base layer, base layer thickness, subbase layer modulus, and base layer modulus are the key factors for mechanical response. A thick base layer and low base and subbase moduli are beneficial for the mechanical response of the pavement structure.
• Based on the principle of optimal mechanical response and considering cost-effectiveness, six recommended HMAC pavement structure configurations for various base-courses are proposed.