Optimization analysis of theoretical maximum specific gravity of asphalt mixtures in segregated areas of asphalt pavements based on asphalt medium method

During the transportation, paving, and compaction of hot mix asphalt aggregate segregation occurs, leading to changes in the theoretical maximum specific gravity (G_mm) of the asphalt mixture. To accurately determine the G_mm of the asphalt mixture after segregation, field samples of the asphalt mixture were collected and analyzed using the ignition method to evaluate the extent of aggregate segregation at different locations (auger and paver overlap zones). The asphalt immersion method was employed to precisely measure the G_mm. Grey relational analysis was applied to identify influencing factors and their patterns of impact on G_mm, and the relational degree of each factor was determined. By introducing weight factors and variation ratios for each factor, an optimized prediction model for G_mm was established. The results indicate that the specific gravity ratio of coarse to fine aggregate is the most significant factor affecting G_mm. The error between the predicted air void content of the asphalt pavement based on the corrected G_mm and the core-measured values obtained via the asphalt immersion method does not exceed 0.5%. This model is suitable for estimating the G_mm of segregated asphalt mixtures, thereby improving the accuracy of compaction quality assessment in segregated areas of asphalt pavements.

1 Introduction

Asphalt pavement is one of the most widely used infrastructure materials worldwide due to its excellent ride quality, durability, and ease of construction and maintenance (Huang et al., 2025; Xiong et al., 2024a; Li et al., 2024). However, the performance and service life of asphalt pavements are highly dependent on the uniformity and quality of the asphalt mixture during construction (Chen et al., 2025; Tan et al., 2025). Among the various challenges affecting pavement quality, aggregate segregation remains a critical yet often overlooked issue (Zhang et al., 2025a; Zhang et al., 2025b; Zhai et al., 2025). Segregation refers to the non-uniform distribution of coarse and fine aggregate particles within the mixture, which typically occurs during production, transportation, placement, and compaction (Fang et al., 2019; Su et al., 2025). This phenomenon can lead to significant variations in the volumetric and mechanical properties of the asphalt layer, ultimately compromising the pavement performance (Xiong and Tan, 2023; Yu et al., 2021).

The occurrence of segregation is often attributed to improper handling during material production and construction processes, such as excessive mixing time, incorrect drop heights during material transfer, and poor paving practices (Xiong et al., 2024b). Segregated areas exhibit higher air void contents, reduced durability, accelerated aging, and increased susceptibility to moisture damage and rutting (Zhang et al., 2024; Sun et al., 2024). Despite advances in paving technology, segregation remains a common problem that is difficult to completely eliminate (Wei et al., 2024; Shi et al., 2023). Current detection methods, such as infrared thermography and laser profiling, provide some means of identifying segregation but often fail to quantitatively assess its impact on key material properties (Xiong et al., 2025; Zeng et al., 2023; Hoang and Tran, 2022). Therefore, there is a pressing need to develop more accurate and practical methods to evaluate and mitigate the effects of segregation, particularly in terms of volumetric properties that directly influence pavement performance.

A key volumetric property significantly affected by segregation is the theoretical maximum specific gravity (G_mm) of the asphalt mixture (Han et al., 2025). G_mm represents the density of the mixture in the absence of air voids and serves as a reference value for calculating air void content, which is a critical indicator of compaction quality (Cao et al., 2026; Phan et al., 2024). The accuracy of Gmm measurement is essential for ensuring the reliability of subsequent performance predictions (Khan et al., 2024). Traditionally, G_mm is determined in the laboratory using the rice test (ASTM D2041) for loose mixtures before compaction (Yan et al., 2021; Aschenbrener and Tran, 2020). However, this method assumes a homogeneous mixture and does not account for changes in aggregate distribution caused by segregation (Xiong et al., 2021).

The accurate measurement of the theoretical maximum specific gravity (Gmm) is fundamental for quantifying segregation, yet conventional methods face significant limitations under such conditions (Aschenbrener and Tran, 2020; Beyene et al., 2024). The standard rice test, while simple and cost-effective (Wu et al., 2019; Kvasnak et al., 2010), is notoriously prone to error when testing segregated mixtures. Its reliance on water as an immersion medium leads to incomplete saturation and inflated Gmm values for highly absorptive aggregates—a common feature in segregated material. Although alternative techniques like the paraffin coating and vacuum sealing methods (Cox and Howard, 2014; Yu et al., 2012) offer improved accuracy by preventing water ingress, their operational complexity and time-consuming procedures render them unsuitable for the rapid, routine assessments required for effective segregation control. The recently proposed asphalt immersion method (Chen et al., 2023; Hussan et al., 2019) presents a promising alternative by using asphalt to mitigate aggregate absorption issues. However, its application is still nascent; a lack of standardized protocols and comprehensive validation across diverse mix designs and segregation scenarios has hindered its widespread adoption (Sebaaly et al., 2018). This critical gap in reliable, practical Gmm measurement for segregated mixtures underscores the necessity of this research, which aims to develop a robust and field-applicable evaluation framework.

The variability of G_mm in segregated mixtures is influenced by multiple factors, including changes in aggregate gradation, binder content, and the specific gravity of individual aggregate fractions (Leiva and West, 2008; Liu et al., 2024). Factors such as the coarse-to-fine aggregate specific gravity ratio, filler content, and asphalt absorption characteristics play significant roles in determining G_mm (Beyene et al., 2024; Nanugonda et al., 2022; Ghos et al., 2022). However, the relationships between these factors and G_mm are not fully understood, particularly in the context of segregation (Jweih and an, 2023). Existing models for estimating G_mm often assume uniform material properties and are therefore inadequate for addressing the complexities introduced by segregation (Dalhat and Osman, 2024; Liu et al., 2022). This highlights the need for a more comprehensive approach that considers the combined effects of key influencing factors and provides a reliable means of predicting Gmm in segregated areas.

In light of the above challenges, this study aims to develop an optimized prediction model for G_mm in segregated asphalt mixtures using the asphalt immersion method and grey relational analysis. The research methodology is illustrated in Figure 1. The specific objectives are: (1) to evaluate the extent of aggregate segregation in different pavement locations, including the auger and paver overlap zones; (2) to accurately determine G_mm using the asphalt immersion method for both designed and segregated mixtures; (3) to identify key factors influencing G_mm and quantify their effects using grey relational analysis; (4) to establish a predictive model for G_mm incorporating weight factors and variation ratios of these influencing factors; and (5) to validate the model by comparing predicted air void contents with core-measured values. The findings of this research are expected to provide a practical tool for improving the accuracy of compaction quality assessment in segregated areas, thereby contributing to enhanced pavement performance and longevity.

Figure 1

Figure 1. Research methodology and analytical procedure.

2 Asphalt pavement materials

2.1 Asphalt binder

The intermediate layer of GAC-20C asphalt concrete employs SBS-modified asphalt (I-D type). The specific test results are presented in Table 1. According to Table 1, the performance indicators of the modified asphalt include a penetration value of 5.45 mm, a ductility of 27 cm, and a softening point of 83.5 °C. Furthermore, other key parameters, such as dynamic viscosity, mass change after aging, and residual ductility, also meet the specifications and technical requirements outlined in relevant standards.

Table 1

Table 1. Technical specifications and test results of SBS (I-D Type) modified asphalt.

Each of these performance indicators plays a critical role in determining the quality and durability of the asphalt mixture. For instance, the penetration value reflects the hardness of the asphalt binder, which is crucial for ensuring adequate resistance to deformation under high-temperature conditions. The ductility value indicates the material’s stretchability and flexibility, which is essential for accommodating stress and strain without cracking, especially in low-temperature environments. The softening point represents the temperature at which the asphalt transitions from a semi-solid to a viscous state, which is vital for evaluating its resistance to high-temperature rutting.

Dynamic viscosity, on the other hand, directly influences the workability and pumpability of asphalt during mixing and paving operations, while the mass change after aging measures the material’s resistance to oxidative aging, which is critical for long-term performance. Residual ductility after aging reflects the asphalt’s ability to retain flexibility and resist cracking after prolonged exposure to environmental factors.

The fact that all these indicators meet the required standards underscores the high quality and reliability of the SBS-modified asphalt used in this study. These properties collectively ensure that the asphalt mixture will deliver excellent performance in terms of structural integrity, fatigue resistance, and longevity, making it a suitable material for high-demand paving applications.

2.2 Aggregates

The GAC-20C medium-graded asphalt mixture is composed of four gradation ranges of aggregate: 0–3 mm, 3–5 mm, 5–10 mm, and 10–20 mm. Each gradation meets the regulatory standards. The coarse aggregate used is diabase, sourced from the Furong Quarry in Linjiang, Heyuan. The coarse aggregate exhibits a crushing value of less than 18% and a flakiness index not exceeding 12%. The fine aggregate has a passing rate of less than 10% for the 0.075 mm sieve. The particle size distribution and other relevant indicators of the mineral filler comply with the standard requirements, as shown in Table 2.

Table 2

Table 2. Technical specifications and test results of mineral filler.

Each of these indicators plays a critical role in determining the quality and performance of the asphalt mixture. The gradation of aggregates directly affects the mixture’s strength, stability, and compactability. Proper gradation ensures an optimal balance between voids and binder content, which is crucial for the durability and load-bearing capacity of the pavement.

The low crushing value of the coarse aggregates indicates high resistance to fragmentation under load, contributing to the structural integrity and longevity of the pavement. The minimal flakiness index ensures that the aggregates have a more cubic shape, which enhances interlocking and stability within the mixture.

The fine aggregate’s low passing rate for the 0.075 mm sieve implies reduced dust and fines content, which helps in achieving better workability and compaction during the laying process. This also minimizes the potential for stripping and moisture damage, thereby enhancing the mixture’s durability.

The compliance of the mineral filler’s particle size distribution and other characteristics with standards is essential for ensuring proper filler-binder interaction, which improves the stiffness and resistance to deformation of the asphalt mixture.

Overall, the adherence to these technical specifications and quality indicators ensures the production of a high-performance asphalt mixture, capable of withstanding various stresses and environmental conditions, thereby extending the service life of the pavement.

2.3 Asphalt mixture proportioning

Through continuous sampling of aggregates during the production process, wash sieving tests and trial mix analyses were conducted for various aggregates. Based on the sieving results, the aggregates were synthesized and proportions adjusted using the composite aggregate gradation curve. The goal was to select a reasonable aggregate gradation curve and adjust the composite gradation to fall within the designed gradation range, ideally close to the median value. The final trial mix results for the designed aggregate gradation composition of the GAC-20C asphalt mixture are shown in Figure 2.

Figure 2

Figure 2. Aggregate gradation curve of GAC-20C asphalt mixtures.

The determination of the optimal aggregate gradation curve is crucial as it directly influences the mixture’s stability, durability, and workability. Proper gradation ensures a balanced distribution of particle sizes, which maximizes density and mechanical interlock, thus enhancing the load-bearing capacity and resistance to deformation of the pavement.

Furthermore, the optimal asphalt content is critical for achieving the desired performance characteristics of the asphalt mixture. For the GAC-20C asphalt mixture, the optimum asphalt content was determined to be 4.3%, resulting in an asphalt-to-aggregate ratio of 4.5%. This precise proportioning ensures sufficient binder to coat the aggregates properly, providing adequate flexibility and resistance to cracking, while also maintaining structural integrity under traffic loads.

3 Engineering application background

This project adopts a dual six-lane expressway standard with a design speed of 120 km/h. The overall width of the embankment is 34.5 m, which includes a 3-meter-wide central median, two 0.75-meter-wide shoulders, two carriageways each consisting of three 3.75-meter-wide lanes, two 3-meter-wide hard shoulders, and two 0.75-meter-wide earth shoulders.

The mainline asphalt pavement structure is designed with a 15 cm thick subbase layer, a 20 cm thick cement-stabilized crushed stone subbase, and two 18 cm thick cement-stabilized crushed stone base layers (upper and lower). The asphalt surface layer configuration includes a 7 cm thick GAC-25 asphalt concrete base layer, a 5.5 cm thick GAC-20C asphalt concrete intermediate layer, and a 4.5 cm thick GAC-16C asphalt concrete surface layer. Additionally, a prime coat and a slurry seal layer are placed between the base and surface layers, and a tack coat is applied between the layers of asphalt concrete.

The precise layering and material specifications are critical to achieving the desired structural integrity, load distribution, and durability of the pavement. The cement-stabilized crushed stone layers provide a robust and stable foundation that enhances the pavement’s resistance to deformation and fatigue. The asphalt concrete layers, with varying gradations and compositions, ensure a balanced combination of flexibility and strength, improving the pavement’s ability to withstand traffic loads and environmental stresses.

The inclusion of the prime coat, slurry seal layer, and tack coat between the layers enhances the bond strength between the layers, reducing the potential for delamination and increasing the pavement’s overall longevity. This meticulous design approach ensures that the pavement structure meets rigorous performance standards, providing a safe and durable roadway for high-speed traffic.

3.1 In-situ air voids in asphalt pavement

In the construction of the GAC-20C asphalt layer using SBS (I-D Type) modified asphalt for the expressway pavement, two pavers were employed in tandem to execute the full-width paving operation. The operation maintained key parameters within stringent limits: a mix temperature of 165 °C–175 °C, a constant paving speed of 2–3 m/min, the compaction performed with several 12-ton vibratory rollers at a frequency of 50 Hz, and achieved a target compaction density of ≥93% of G_mm for both pavers, ensuring a uniform and homogeneous mat. Upon completion of paving, non-nuclear density measurements were conducted over the entire cross-section to determine the in-situ density of the asphalt layer. A representative 50-meter segment of the intermediate asphalt layer in the right-hand lane (K130 + 000–050), with a width of 13 m, was selected for detailed analysis. A square grid system was established on the pavement surface to define measurement points, with both longitudinal and transverse intervals set at 0.25 m. A 0.5 m wide strip along both edges was excluded from measurements.

Based on the collected density data and the design theoretical maximum specific gravity value of 2.711, the air void content at each measurement point was calculated. These values were used to generate a grayscale cloud map representing the spatial distribution of air voids throughout the pavement section, as presented in Figure 3.

Figure 3

Figure 3. Grayscale map of measured air void contents for the GAC-20C intermediate asphalt layer.

Analysis of the void distribution revealed that 32% of the measured points exhibited air void contents between 0% and 3%, while 62.9% of points fell within the 3%–6% range. Additionally, 5.1% of points demonstrated void contents ranging from 6% to 9%, with recorded extremes of 8.85% and 0.34%. Comparison with visual observations of the pavement surface (Figure 4) indicated concordance between the pattern of macro-scale voids (indicative of aggregate segregation) and the distribution trend derived from non-nuclear density measurements.

Figure 4

Figure 4. GAC-20C intermediate asphalt layer surface.

To evaluate the influence of aggregate segregation on theoretical maximum specific gravity of asphalt mixture, samples of asphalt mixtures were obtained from behind the paver prior to compaction at three distinct locations: the central portion of the paver, the vicinity of the spiral distributor, and the overlapping zone between the two pavers. These samples underwent ignition sieve analysis under laboratory conditions. Furthermore, core samples were extracted from corresponding locations after paving and density testing for validation purposes.

For analytical consistency, the spiral distributor location was defined as the region within 1.0 m of each paver end, with the remaining area designated as the central zone. The overlapping zone between the two pavers was maintained at 0.5 m width. Interestingly, the grayscale representation in Figure 3 suggests a lower air void content within the overlap zone compared to adjacent areas—an observation that contradicts typical engineering expectations. This anomaly is hypothesized to result from a synergistic compaction effect. The trailing paver, acting on the already pre-compacted mat from the leading paver, may subject the overlap zone to a secondary and prolonged kneading action. This process potentially leads to particle rearrangement and a further reduction of air voids, overriding the tendency for segregation or inadequate compaction that might otherwise be expected at such joints. Further investigation will be conducted to elucidate the mechanisms underlying this unexpected phenomenon.

3.2 Analysis of aggregate gradation in field asphalt mixtures

As shown in Figure 3, asphalt mixture samples were collected from different locations corresponding to the two pavers and subjected to laboratory ignition sieve analysis to determine aggregate gradation. The results are presented in Table 3. The mass passing percentage of the aggregate through the 4.75 mm sieve remained relatively consistent across all sampling locations. In contrast, considerable variation was observed in the passing rate through the 9.5 mm sieve: the value increased in the middle section between the two pavers—though it remained within the specification-recommended range—while it decreased at the left and right spiral distributor locations of both pavers, even falling outside the allowable range in some cases. The passing rates of the 13.2 mm and 16 mm sieves were influenced by that of the 9.5 mm sieve, also exceeding the specified limits in several instances.

Table 3

Table 3. Mass passing percentage of aggregate for each sieve size after laboratory burn-off of asphalt mixture (unit: %).

To better understand the segregation of aggregates in the asphalt mixture, the deviations between the measured mass retention rate on each sieve and the design values were calculated, as summarized in Table 4. Little variation was found in the mass fractions of aggregates smaller than 4.75 mm, though the fraction in the 2.36–4.75 mm range showed the most noticeable change among fine aggregates. For aggregates larger than 4.75 mm: in the middle zone of the paver, the mass fraction of the 4.75–9.5 mm fraction increased, while the fractions retained on sieves larger than 9.5 mm decreased. In contrast, the opposite trend was observed at the spiral distributor locations. In the overlap zone between the two pavers, all fractions smaller than 9.5 mm decreased—with the most significant reduction in the 4.75–9.5 mm range—while all coarser fractions increased. These results indicate that fine segregation occurred to some extent in the middle zone of the paver, whereas coarse segregation was observed at both the spiral distributor and the overlap zones.

Table 4

Table 4. Difference between the aggregate’s sieve retention rate for the asphalt mixtures of different zones and the design value for each sieve size (unit: %).

By integrating the findings from Figure 3 and Table 4, it can be concluded that the aggregate segregation exhibited a symmetric pattern along the centerline of the pavers. Although the variations in aggregate fractions were very similar in the middle zones of both Pavers 1 and 2, the in-place air void content of the pavement corresponding to the middle zone of Paver No. 2 was lower than that of Paver No. 1. This suggests that, in addition to segregation during paving, compaction-induced segregation also contributed to the final distribution of air voids. Furthermore, since the sampled locations were limited only to the “immediate center” behind the paver and the number of samples was insufficient, the results may not fully represent the entire middle zone of the paver. Therefore, the effect of fine segregation on the theoretical maximum specific gravity was not considered in this analysis. To clarify the influence of coarse segregation on the theoretical maximum specific gravity, a follow-up study will be conducted to analyze the factors affecting this parameter in asphalt mixtures.

4 Asphalt medium method for G_mm of asphalt mixtures

Currently, the theoretical maximum specific gravity (G_mm) of asphalt mixtures is commonly determined using the vacuum sealing method and the solvent method. The vacuum method employs water as the medium; however, due to the presence of closed voids within the loose mixture, the measured values tend to be theoretically lower than the actual value. The solvent method, which uses trichloroethylene to dissolve the asphalt, may lead to overestimation since the solvent can penetrate open voids in the aggregate that are not filled with asphalt. Both methods, along with direct calculation approaches, derive a constant Gmm value under laboratory conditions using loose mixtures. This value is subsequently used to calculate the compactness or air void content of Marshall specimens or field cores obtained from the paved layer on the same day.

However, these conventional methods do not account for variations caused by aggregate segregation during mixing, transportation, paving, and compaction, nor do they consider the absorption of asphalt by aggregates. These factors contribute to significant variability in the actual G_mm of the asphalt mixture, implying that the conventional theoretical values are inherently inaccurate.

In this study, asphalt itself is utilized as the immersion medium to directly determine the G_mm of Marshall specimens or field cores. This approach ensures that the measured air void content approximates zero more realistically, thereby improving accuracy and enhancing the representativeness of the results.

1. Apparatus for asphalt immersion method

Several 1,000 mL beakers, stainless steel stirrers, laboratory oven, full set of equipment for underwater weighing method.

2. Experimental procedure of asphalt immersion method

a. a. Weigh the empty mass of Beaker 1 with the stirrer in air (M₁) and in water (M₂). Weigh the empty mass of Beaker 2 (used for determining asphalt density) in air (M₃) and in water (M₄).

b. b. Heat and break the Marshall specimen into loose mixture. Place Beaker 1 with the stirrer on the scale, tare, then add the mixture and record its mass (M₅).

c. c. Place Beaker 1 containing the mixture and stirrer into an oven preheated to 160 °C (140 °C for unmodified asphalt) for 0.5 h.

d. d. After 0.5 h, remove Beaker 1. Pour preheated asphalt of the same type into Beaker 1 and stir immediately with the stirrer to ensure thorough incorporation into the mixture. Simultaneously, pour asphalt into empty Beaker 2 without stirring. Place both beakers into a 140 °C oven. Every 15 min, remove Beaker 1 and stir for 3 min. Repeat this at least three times until no significant air bubbles are observed. Then place Beaker 1 into a 160 °C oven (140 °C for unmodified asphalt) and let it stand for 1 h. If no surface bubbles are present, remove both beakers and allow them to cool to room temperature.

e. e. Weigh Beaker 1 containing the asphalt mixture and stirrer in air (M₆) and in water (M₇). Weigh Beaker 2 containing only asphalt in air (M₈) and in water (M₉).

f. f. The specific gravity of asphalt (G_b) and the theoretical maximum specific gravity of the asphalt mixture (G_mm) are calculated using Equation 1 and Equation 2, respectively.

$G_b=\frac{M_8-M_3}{\left(M_8-M_9\right)-\left(M_3-M_4\right)}(1)$

$G_{\text{mm}}=\frac{M_5}{\left(M_6-M_7\right)-\left(M_1-M_2\right)-\left(M_6-M_1-M_5\right)/G_{\mathrm{b}}}(2)$

a. g. The air void content (VV) of the asphalt mixture Marshall specimen or core sample is calculated using Equation 3.

$VV=\left(1-G_{\text{mb}}/G_{\text{mm}}\right)\times 100(3)$

where G_mb denotes the bulk specific gravity of the asphalt mixture sample.

This refined approach, employing asphalt as the medium, ensures a more accurate determination of the theoretical maximum specific gravity. It accounts for the elimination of voids, providing a more representative and precise measure, crucial for evaluating the compaction and voids of asphalt mixtures. This method enhances the accuracy and representativeness of the data, leading to more reliable assessments of asphalt mixture performance and quality control in pavement construction.

5 Factors affecting G_mm of asphalt mixtures

5.1 Experimental design

The experimental design was developed to investigate factors influencing the theoretical maximum specific gravity (G_mm) of asphalt mixtures. The considered variables included: asphalt-to-aggregate ratio (Factor 1, %), specific gravity ratio of coarse to fine aggregate (Factor 2), specific gravity of asphalt binder (Factor 3), mass fraction of particles smaller than 4.75 mm (Factor 4, %), mass fraction of particles smaller than 2.36 mm (Factor 5, %), and filler content (Factor 6, %).

Aggregates were diabase and limestone sourced from the Heyuan Furong Quarry, with gradations of 0–3 mm, 3–5 mm, 5–10 mm, 10–15 mm, 15–20 mm, and 20–25 mm. The mineral filler was limestone powder. The binders used included neat 70# asphalt and SBS-modified asphalt.

Aggregate gradations followed the upper specification limit, design value, and lower specification limit for GAC-16C and GAC-20C mixtures. The design asphalt-to-aggregate ratio was 4.5% for GAC-20C and 4.8% for GAC-16C.

To evaluate the effect of asphalt specific gravity, binders from several manufacturers—both modified and neat—were employed. Different lithologies of coarse and fine aggregates were combined to examine the influence of aggregate density variations. Additional mixtures with varying asphalt contents were prepared to assess the impact of asphalt-to-aggregate ratio. Multiple Marshall mix designs were developed accordingly, with detailed experimental parameters provided in Table 5. For each mix, five Marshall specimens were fabricated for subsequent testing and analysis.

Table 5

Table 5. Experimental conditions and test results of asphalt mixture Marshall specimens.

Given the dense and semi-dense nature of the mixtures, the bulk specific gravity (G_mb) of the Marshall specimens was determined using the saturated surface-dry (SSD) method. The theoretical maximum specific gravity (G_mm) was measured via the asphalt immersion method.

The final G_mm value for each mixture was represented by the average of at least three consistent measurements from the five replicates, with minimal deviation among them. Processed results of the maximum theoretical density are summarized in Table 5. Figure 5 illustrates the prepared Marshall specimens and the actual testing process using the asphalt immersion method.

Figure 5

Figure 5. (a) Marshall specimens of asphalt mixtures; (b) Determination of theoretical maximum specific gravity using the asphalt immersion method.

In Table 5, the same limestone mineral filler was used for each set of Marshall specimens of asphalt mixtures. The designation “Diabase + Limestone” indicates that coarse aggregates larger than 4.75 mm consisted of limestone, while fine aggregates between 0.075 mm and 4.75 mm were composed of diabase. Conversely, “Limestone + Diabase” denotes that coarse aggregates larger than 4.75 mm were diabase, and fine aggregates between 0.075 mm and 4.75 mm were limestone.

When only the asphalt-to-aggregate ratio was varied, the theoretical maximum specific gravity of the asphalt mixture decreased as the ratio increased. When only the aggregate gradation was altered, the theoretical maximum specific gravity increased as the proportion of fine aggregates decreased. Although certain general trends can be inferred from Table 5, the presence of multiple influencing factors, the considerable volume of data, and significant variability make it difficult to identify the dominant factors affecting the theoretical maximum specific gravity of the asphalt mixture.

5.2 Grey relational analysis of factors influencing G_mm of asphalt mixtures

Grey system theory provides a methodology for processing limited and seemingly irregular data to uncover inherent characteristics of a system. Grey relational analysis (GRA), as a form of systemic factor analysis, is used to evaluate the degree of correlation among various factors within a system. The fundamental principle involves comparing the geometric similarity between a reference sequence and comparative sequences. The closeness of their curves reflects the degree of relational similarity, indicating how strongly the factors are associated.

The strength of these relationships is quantified using a relational grade, which describes the extent of influence each factor has on the outcome—a higher relational grade signifies a greater degree of influence. The computational procedure generally involves the following steps: dimensionless data processing, selection of comparative sequences, construction of difference sequences, calculation of grey relational coefficients, and finally, determination of the grey relational grade. Accordingly, grey relational analysis was applied to process the data presented in Table 5 to identify key influencing factors.

1. Calculation steps and formulas for grey relational analysis

a. a. First, a reference data series is defined. Consider a set of discrete sequences:

$x_0\left(k\right),k=1,2,\cdots ,m$

$x_i\left(k\right),k=1,2,\cdots ,m;i=1,2,\cdots ,n$

where $x_0\left(k\right)$ represents the mother sequence (i.e., the primary factor or objective of the study), $x_i\left(k\right)$ denotes the child sequences (i.e., influencing factors or comparative series).

b. b. Prior to calculating the relational coefficients and relational degree, the data must be normalized to eliminate dimensional effects. The mean normalization method can be applied, as shown in Equations 4, 5. They normalize the data by converting each factor to a dimensionless value within a specific range, typically [0, 1]. This ensures comparability among different factors.

$y_0=\frac{x_0\left(k\right)}{{\displaystyle {\sum }_{k=1}^m}{x}_0\left(k\right)/m}k=1,2,\cdots ,m(4)$

$y_i=\frac{x_i\left(k\right)}{{\displaystyle {\sum }_{k=1}^m}{x}_i\left(k\right)/m}k=1,2,\cdots ,m;i=1,2,\cdots ,n(5)$

a. c. The relational coefficient is calculated as shown in Equation 6:

$\lambda \left(k\right)=\frac{\underset{i}{\min }\left\{\underset{k}{\min }\left|y_0\left(k\right)-y_i\left(k\right)\right|\right\}+\alpha \underset{i}{\max }\left\{\underset{k}{\max }\left|y_0\left(k\right)-y_i\left(k\right)\right|\right\}}{\left|y_0\left(k\right)-y_i\left(k\right)\right|+\alpha \underset{i}{\max }\left\{\underset{k}{\max }\left|y_0\left(k\right)-y_i\left(k\right)\right|\right\}}(6)$

where α denotes the resolution coefficient, typically selected within the range of 0–1. The resolution coefficient (α = 0.5) was selected as it is the most common and neutral value used in grey relational analysis, minimizing bias towards either maximizing or minimizing the relational grade. λ(k) represents the relational coefficient of the i-th factor at the k-th point, which reflects the relative difference between the comparative curve y_i(k) and the reference curve y₀(k).

Since the direct use of relational coefficient values often results in numerous and dispersed data, which complicates comparison, it is necessary to aggregate the coefficients across all time points into a single representative value. Averaging the coefficients is a common method to consolidate such distributed information into a unified metric.

a. d. The formula for calculating the grey relational degree is given by Equation 7:

$r_i=\frac{1}{m}{\displaystyle \sum _{k=1}^m}{\lambda }_i\left(k\right)k=1,2,\cdots ,m;i=1,2,\cdots ,n(7)$

where r_i denotes the grey relational degree between curve yᵢ and the reference curve y₀. The sequence of relational degrees rᵢ illustrates the extent of influence each factor exerts on the outcome.

1. 2. Grey relational degree calculation of factors influencing G_mm of asphalt mixture

Following the calculation procedure outlined in Section 1, the data from Table 5 were first normalized, with the results presented in Table 6. To compute the grey relational degree, the difference sequences between each influencing factor and the reference sequence were calculated, as summarized in Table 7. The grey relational coefficients for each influencing factor were subsequently determined and are listed in Table 8.

Table 6

Table 6. Initialization of experimental results for each influencing factor.

Table 7

Table 7. Difference sequence of each influencing factor.

Table 8

Table 8. Grey relational coefficient of each influencing factor.

The average values of the grey relational coefficients for each factor were calculated from the grey relational analysis results of Marshall specimens 1–20 in Table 8, and are summarized in Table 9. The influencing factors were ranked in descending order of their impact on the theoretical maximum specific gravity of the asphalt mixture as follows: specific gravity ratio of coarse to fine aggregate, filler content, asphalt-to-aggregate ratio, asphalt specific gravity, followed by the content of aggregate particles smaller than 2.36 mm and those smaller than 4.75 mm.

Table 9

Table 9. Mean value of grey relational coefficients for each influencing factor of G_mm of asphalt mixture specimens.

The specific gravity ratio of coarse to fine aggregate was identified as the most significant factor, indicating that the specific gravity of the aggregate is the primary variable affecting the theoretical maximum specific density of the asphalt mixture, which is consistent with intuitive analytical expectations.

Although filler accounts for a small proportion of the mixture, it exerted a considerable influence. This can be attributed to the high specific surface area of fine particles, which enables greater asphalt adsorption. When the filler-asphalt ratio is constant, an increase in filler content requires a corresponding increase in asphalt content. Furthermore, finer particles enhance the filling effect within the asphalt mixture. The asphalt-to-aggregate ratio, which determines the amount of asphalt used, interacts synergistically with filler content, resulting in a similar degree of influence.

Although the specific gravity of asphalt itself exhibited minimal variation—fluctuating around 1.03—its impact was greater than that of the contents of particles smaller than 2.36 mm and 4.75 mm. This observation may be related to the penetration grade of asphalt and the asphalt absorption coefficient of the blended aggregate.

The contents of particles smaller than 2.36 mm and 4.75 mm had the least influence. This is partly because the calculated values for these fractions already include the filler content, which appears to be the dominant factor within the fine aggregate portion. Moreover, the limited variability in density among different aggregate fractions reduced the effect of changes in fine aggregate proportion, making it less influential than the specific gravity of the aggregate itself.

6 Optimization analysis of G_mm of asphalt mixtures

6.1 Correction of G_mm of asphalt mixtures

Through ignition sieve analysis of asphalt mixtures, it was confirmed that the aggregate gradation of field asphalt mixtures changes after segregation, consequently altering the theoretical maximum specific gravity (G_mm) of the corresponding mixture. Based on the grey relational analysis of influencing factors presented in the previous section, the grey relational coefficients and the degree of influence of each factor on the Gmm were determined.

By comprehensively considering the grey relational coefficients of all factors, the proportional contribution of each factor to the overall influence can be interpreted as its weight factor affecting the G_mm. The sum of these weight factors is equal to 1. Given that the design theoretical maximum specific gravity of the intermediate layer asphalt mixture in the field pavement is 2.711, the modified equation for the Gmm can be expressed as follows Equation 9.

$G_{\text{mm}}=G_{{\text{mm}}_{\mathrm{d}}}\times {\displaystyle \sum _{i=1}^n}\left({\beta }_i\times {\lambda }_i\right)=2.711\times {\displaystyle \sum _{i=1}^n}\left({\beta }_i\times {\lambda }_i\right),i=1,2,\cdots ,n(8)$

where G_{mm_d} indicates the design value of the theoretical maximum specific gravity for asphalt mixtures. β_i represents the dimensionless variation ratio of each factor between the segregated condition and the original design gradation. λ_i denotes the dimensionless weight factor of each influencing factor, ensuring that the sum of all λ_i equals 1. These factors are crucial for accurately modeling the impact of segregation on material properties.

1. Calculation of influence weight factors λ

The influence weight factors λ were derived from the grey relational coefficients of each influencing factor presented in Table 9. To minimize rounding errors in calculations, the weight factors were retained to four decimal places. The resulting values of the influence weight factors are summarized in Table 10.

1. 2. Factor variations in asphalt mixture before and after segregation

Table 10

Table 10. Influence weight factors of various factors affecting the G_mm of asphalt mixtures.

Due to the symmetrical distribution of aggregate segregation during asphalt pavement paving, and considering the similar segregation characteristics of the asphalt mixture at different positions of the paver, the sieve retention rates of the mixture from various positions of the two pavers were averaged to reduce data variability. The averaged values were then compared with the design sieve retention rates to calculate the deviations. Based on a comprehensive analysis of the data in Table 4, the variations in the sieve retention rates of the segregated mixture at the paver auger location and the paver overlap zone, relative to the design gradation sieve retention rates, were determined and are presented in Table 11.

Table 11

Table 11. Difference between the aggregate’s sieve retention rate after segregation and the design value for each sieve size (unit: %).

Regarding the specific gravity ratio of coarse to fine aggregate, since the specific gravity of each fraction of aggregate remains unchanged, the segregation of the asphalt mixture only alters the proportion of each fraction, while the specific gravities of the coarse and fine aggregates remain essentially constant. Consequently, this ratio also remains largely invariant.

Given that the asphalt used at the construction site remains consistent, the specific gravity of the asphalt was considered unchanged and adopted as 1.036. Based on the data in Table 11, the proportions of each aggregate fraction after segregation were calculated, thereby obtaining the post-segregation values for the content of particles smaller than 4.75 mm, particles smaller than 2.36 mm, filler content, and the asphalt-to-aggregate ratio. The relevant results are presented in Table 12.

1. 3. Correction of G_mm for segregated asphalt mixtures considering influencing factors

Table 12

Table 12. Values of each influencing factor in the design gradation and post-segregation state of asphalt mixture.

As summarized in the aforementioned Table 5, an increase in the asphalt-to-aggregate ratio leads to a decrease in the theoretical maximum specific gravity of the asphalt mixture. Conversely, an increase in the specific gravity of the asphalt binder results in an increase in the theoretical maximum specific gravity of the mixture. Furthermore, a higher proportion of fine aggregates contributes to a reduction in the theoretical maximum specific gravity, while increased filler content and asphalt-to-aggregate ratio also diminish this value.

Based on the experimental results, the influence weight factors (λ) from Table 10 and the factor variations (Δ) before and after segregation from Table 12 were incorporated into Equation 8. This integration yields a corrected formula (Equation 9) for estimating the theoretical maximum specific gravity of the asphalt mixture following aggregate segregation. The effects of the individual or combined factors are already expressed in Equation 9.

Based on the aforementioned calculations, the modified theoretical maximum specific gravity for the intermediate layer GAC-20C asphalt pavement was determined. The results indicate that the theoretical maximum specific gravity of the asphalt mixture at the auger location is 2.768, while that at the paver overlap zone reaches 2.788.

Incorporating these results into the analysis provides a comprehensive understanding of how various factors affect the theoretical maximum specific gravity of asphalt mixtures. The corrected formula accounts for changes due to segregation, ensuring more accurate predictions of the asphalt mixture’s performance in practical applications. This approach highlights the importance of considering both the specific gravity of asphalt and aggregates, as well as the proportions of fine aggregates and mineral powders, in the design and evaluation of asphalt mixtures.

$\begin{array}{l}{G}_{\text{mm}}=G_{{\text{mm}}_{\mathrm{d}}}\times \left(\frac{{\Delta }_{1_{\mathrm{d}}}}{{\Delta }_1}\times {\lambda }_1+\frac{{\Delta }_2}{{\Delta }_{2_{\mathrm{d}}}}\times {\lambda }_2+\frac{{\Delta }_3}{{\Delta }_{3_{\mathrm{d}}}}\times {\lambda }_3+\frac{{\Delta }_{4_{\mathrm{d}}}}{{\Delta }_4}\times {\lambda }_4+\frac{{\Delta }_{5_{\mathrm{d}}}}{{\Delta }_5}\times {\lambda }_5+\frac{{\Delta }_{6_{\mathrm{d}}}}{{\Delta }_6}\times {\lambda }_6\right)\\ =2.711\times \left(\frac{4.5}{{\Delta }_1}\times {\lambda }_1+\frac{{\Delta }_2}{1.016}\times {\lambda }_2+\frac{{\Delta }_3}{1.036}\times {\lambda }_3+\frac{33.2}{{\Delta }_4}\times {\lambda }_4+\frac{25.6}{{\Delta }_5}\times {\lambda }_5+\frac{6.2}{{\Delta }_6}\times {\lambda }_6\right)\end{array}(9)$

where Δ_{i_d} and Δ_i represent the values of each influencing factor before and after aggregate segregation in the asphalt mixture, respectively, as provided in Table 12.

6.2 Validation analysis of the modified G_mm for segregated asphalt mixtures

Although the theoretical maximum specific gravity of the segregated asphalt mixture was derived using Equation 9, the accuracy of this corrected value requires further validation. To this end, core samples were drilled from the paved and compacted asphalt pavement (as shown in Figure 3), and the theoretical maximum specific gravity of these cores was experimentally determined using the asphalt immersion method. The measured values were then compared with the corrected theoretical maximum specific gravity obtained from the model. It should be noted that the locations selected for coring in the compacted pavement corresponded precisely to the pre-compaction sampling positions in the paving direction, ensuring spatial consistency in the data comparison. The results are presented in Table 13.

Table 13

Table 13. G_mm of asphalt mixture cores based on asphalt immersion method.

This approach provides a thorough verification process by comparing measured values from actual core samples with the theoretically corrected values, thus ensuring the reliability of the correction method for the theoretical maximum specific gravity of asphalt mixtures after segregation.

The variation in asphalt pavement air void content serves as a key indicator for evaluating the necessity of correcting the theoretical maximum specific gravity (G_mm) of the asphalt mixture. For the GAC-20C intermediate layer, the design air void range is 3%–6%, with an allowable variation amplitude of 3%. The design value of G_mm is 2.711. When the pavement air void content is 4.5%, the bulk specific gravity (G_mb) of the mixture, back-calculated using Equation 3, is 2.589.

By replacing the design Gmm value with the corrected values at different pavement locations, the air void content was recalculated, and the results are presented in Table 14. A comparison between the core-measured and the corrected air void contents shows: In the auger zone, the difference is 0.24%, accounting for 8% of the allowable variation amplitude. In the paver overlap zone, the difference is 0.37%, representing 12.3% of the allowable amplitude. The minor discrepancies between the measured and corrected values confirm the feasibility and reliability of the correction method proposed in Equation 9.

Table 14

Table 14. Comparison of air void content in asphalt mixture under design and segregated conditions.

Furthermore, the corrected air void contents are significantly higher than the design value: In the auger zone, the deviation is 1.97%, constituting 65.67% of the allowable amplitude. In the paver overlap zone, the deviation reaches 2.64%, accounting for 88.33% of the allowable amplitude. The substantial proportion of the allowable variation amplitude occupied by these deviations underscores the importance of correcting the G_mm in areas affected by coarse segregation.

Accordingly, the G_mm values in the auger zone and the paver overlap zone were corrected from the fixed design value to 2.768 and 2.788, respectively. The revised grayscale map of air void distribution for the GAC-20C intermediate layer is shown in Figure 6. Areas marked in blue represent the auger zone, where the average air void content increased from 4.62% to 6.59% after correction. Areas marked in red indicate the paver overlap zone, where the average value rose from 4.08% to 6.73%. These results demonstrate that after correcting the Gmm, the air void content increased beyond the design specification in both zones. Therefore, without this correction, preliminary inspection results (e.g., Figure 3) would misleadingly suggest that air void contents in both the auger and overlap zones were within the design range, falsely indicating an absence of segregation. This misinterpretation could compromise construction quality control by overlooking critical defects.

Figure 6

Figure 6. Corrected grayscale map of air void contents for the GAC-20C intermediate asphalt layer.

7 Conclusion

Based on the asphalt immersion method and grey relational analysis, an optimized prediction model was developed to estimate the theoretical maximum specific gravity (G_mm) of asphalt mixtures in segregated pavement areas. The following conclusions are drawn.

1. Aggregate segregation during construction significantly alters mixture composition, resulting in measurable changes in G_mm. The asphalt immersion method proves effective for accurate G_mm determination in field-produced mixtures from segregated zones.

2. Grey relational analysis identifies the specific gravity ratio of coarse to fine aggregate as the most influential factor affecting G_mm. Filler content, asphalt-to-aggregate ratio, and asphalt specific gravity demonstrate secondary influences, while the contents of particles smaller than 2.36 mm and 4.75 mm show minimal effects.

3. The developed model, incorporating weight factors (λ) and variation ratios (β) of key factors, enables precise estimation of G_mm in segregated asphalt mixtures. Validation shows that air void content predictions using corrected G_mm values exhibit less than 0.5% error compared to core-measured values obtained via the asphalt immersion method.

4. Implementation of corrected G_mm values for GAC-20C pavement, specifically 2.768 for auger locations and 2.788 for paver overlap zones, enables more accurate assessment of in-place air void content. Uncorrected evaluations risk misleading compliance interpretations that may conceal construction quality issues. This methodology improves compaction quality assessment accuracy in segregated areas and provides a practical tool for evaluating pavement uniformity.

8 Limitations and future work

This study has several limitations that should be addressed in future research. First, the proposed model was developed and validated using specific mixture types (GAC-16C and GAC-20C) under controlled field conditions. Its applicability to other asphalt mixtures with different gradations or modified binders requires further verification. Second, the model relies on laboratory-measured parameters such as the specific gravity ratio and filler content, which may not be readily available in real-time during construction. Third, the analysis focused primarily on volumetric properties without fully considering the effects of segregation on mechanical performance parameters such as fatigue resistance and durability. Future work will include an assessment of mechanical properties, such as the modulus of elasticity and fatigue life, to provide a more complete analysis of the consequences of segregation.

Future work should focus on extending the model’s applicability to a wider range of asphalt mixtures, including those with polymer-modified binders and recycled materials. Additionally, developing non-destructive testing methods and integrating sensor-based technologies for real-time monitoring of segregation and G_mm correction will be explored to enhance practical implementation. Further investigations should also explore the relationship between corrected G_mm values and mechanical performance indicators to comprehensively evaluate the impact of segregation on long-term pavement behavior. Finally, machine learning techniques could be employed to refine the prediction model using larger and more diverse datasets, improving its accuracy and robustness under varying field conditions.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

Author contributions

YW: Conceptualization, Formal Analysis, Methodology, Writing – original draft. YX: Data curation, Investigation, Writing – original draft. JL: Data curation, Resources, Writing – original draft. KW: Data curation, Investigation, Writing – original draft. BC: Funding acquisition, Resources, Visualization, Writing – review and editing. XC: Data curation, Validation, Writing – original draft. SS: Conceptualization, Formal Analysis, Software, Writing – review and editing. QH: Validation, Visualization, Writing – original draft. WL: Resources, Visualization, Writing – review and editing. XX: Conceptualization, Funding acquisition, Writing – review and editing.

Funding

The authors declare that financial support was received for the research and/or publication of this article. This research was funded by Guangdong Basic and Applied Basic Research Foundation (grant number: 2024A1515110192), National Natural Science Foundation of China (grant number: 52508490), Guangdong Basic and Applied Basic Research Foundation (grant number: 2024A1515110112), Guangdong University Student Science and Technology Innovation Cultivation Special Fund (grant number: pdjh2025bk233), National Key Research and Development Program of China (grant number: 2024YFE0216800), and Youth Science and Technology Talent Development Program of Guangdong Association for Science and Technology (grant number: SKXRC202504).

Conflict of interest

Authors YW, YX, JL, and KW were employed by Poly Changda Engineering Co., Ltd.

The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The authors declare that no Generative AI was used in the creation of this manuscript.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher’s note

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