Performance Enhancement and Nano-Scale Interaction Mechanism of Asphalt Modified with Solid Waste-Derived Nano-Micro-Powders

Abstract

To investigate the influence patterns and underlying mechanisms of solid waste-derived Nano-Micro-Powder (NMP) materials on asphalt performance, this study selected nano-sized silica fume (a typical industrial solid waste) along with conventionally used hydrated lime and cement powders as representative modifiers. Based on material type, dosage, and particle size, the high-temperature rheological properties, low-temperature rheological behavior, and nano-scale mechanical characteristics of NMP-modified asphalt were systematically evaluated through dynamic shear frequency tests, Multiple Stress Creep Recovery (MSCR) tests, Bending Beam Rheometer (BBR) tests, and Atomic Force Microscopy (AFM) measurements. Additionally, the grey relational analysis method was employed to quantify the impact of key nanoparticle characteristics on modified asphalt performance. The results demonstrate the following: (1) With increasing NMP dosage and decreasing particle size, the complex modulus (G*) of modified asphalt increases significantly, while the creep recovery rate (R) rises and non-recoverable creep compliance (J_nr) decreases. The creep stiffness slope (m-value) diminishes under low-temperature conditions. (2) Among different NMP types, silica fume-modified asphalt exhibits the highest G*, R, and m-value parameters. (3) At the nanoscale, adhesion force, modulus, and surface roughness all increase with higher NMP dosage and smaller particle size. Silica fume demonstrates superior performance in these nano-mechanical properties compared to hydrated lime and cement powders. (4) Grey relational analysis reveals that specific surface area shows the strongest correlation with the overall performance of NMP-modified asphalt.

1. Introduction

Asphalt pavement has become the dominant structure for high-grade roads due to its superior riding quality and rapid constructability. The service performance of asphalt pavement is primarily determined by the material composition of its mixture, which consists of two fundamental components: adhesive asphalt binder and load-bearing aggregate skeleton. Among these, the adhesive properties of asphalt binder play a decisive role in overall pavement performance. As a typical viscoelastic material, asphalt exhibits significant temperature dependency—excessive deformation and flow occur under high summer temperatures, leading to permanent rutting, while embrittlement and cracking arise under low winter temperatures [1,2]. These temperature-induced distresses severely compromise the durability and service life of asphalt pavements. To address these limitations, performance enhancement of original asphalt through modifier incorporation has emerged as the most widely adopted strategy in modern pavement engineering [3,4,5,6].

In recent years, scholars have investigated the modification effects of inorganic additives on asphalt properties. Particularly, with green development and environmental sustainability emerging as key priorities in modern highway engineering, the recycling of domestic and industrial solid wastes has become a research hotspot in the field of novel road materials [7]. For instance, Liu and Jia et al. [8,9] prepared asphalt mixtures using nano-sized industrial silica fume (SF) and demonstrated its effectiveness in improving high-temperature rutting resistance and fatigue performance, with smaller particle sizes yielding superior modification effects. Zhang et al. [10] enhanced red mud (RM)-based asphalt mastic using cement as a modifier, systematically evaluating the rheological behavior and interfacial adhesion of both raw and modified RM via Quality Control Tester (QCT) and PosiTest AT-A pull-off tests. Guo and Arabani et al. [11,12] assessed the high-temperature performance of graphene-tourmaline composite micropowder (GTCM), spent coffee grounds (SCG), and fly ash-modified asphalts under varying temperatures and frequencies through dynamic shear rheometry (DSR). Their findings revealed that GTCM-modified asphalt exhibited significantly lower temperature susceptibility and superior aging resistance compared to tourmaline-modified counterparts, while SCG effectively enhanced both high-temperature stability and fatigue endurance. Ou et al. [13] developed a novel warm-mix asphalt (WMA) additive utilizing the crystalline water in phosphogypsum (PG), validating its feasibility as a sustainable WMA solution. Wang et al. [14] developed a multifunctional asphalt mixture (MAM) by incorporating steel slag (SS) aggregates and carbon fiber (CF) additives. The integration of SS and CF significantly enhanced the electrical conductivity of the asphalt mixture, providing the essential electro-mechanical foundation for crack monitoring functionality in MAM. Aboelmagd and Cao et al. [15,16] investigated the modification effects of silica fume (SF) on asphalt binders. Their findings demonstrated that SF-modified asphalts exhibited significant improvements in physical rheological properties, temperature susceptibility, and rutting resistance. Meanwhile, Ran et al. [17] evaluated the moisture susceptibility and rheological performance of hydrated lime-modified oil sludge pyrolysis residue (OPR) asphalt emulsions across temperature ranges using Bending Beam Rheometer (BBR) and Dynamic Shear Rheometer (DSR) tests.

With the advancement of next-generation micro-nano characterization techniques, research focusing on micro-nano scale analysis of asphalt surface morphology and mechanical properties to elucidate modification mechanisms has proliferated, particularly employing atomic force microscopy (AFM) for nanoscale surface topography scanning [18]. Ming et al. [19] investigated the effects of inorganic montmorillonite (MMT) and organophilic montmorillonite (OMMT) as asphalt modifiers on adhesive interactions between asphalt and aggregates. Their findings revealed that MMT/OMMT incorporation increased the surface free energy (SFE), dispersive component, and polar fraction of asphalt, thereby enhancing its bonding capacity. Yu and Almashaqbeh et al. [20,21] employed atomic force microscopy (AFM) to investigate the effects of graphene (GN) and graphene oxide (GO) on asphalt surface roughness and peak-force variations, providing nanoscale insights into the microstructural reinforcement mechanisms during asphalt modification.

Extensive research has been conducted by domestic and international scholars on the performance modification of asphalt using solid waste NMP. However, a unified consensus has yet to be established regarding the core characteristic parameters of solid waste NMP that influence asphalt properties. Moreover, existing studies predominantly focus on macroscopic performance evaluations across different waste materials, particle sizes, and dosages, lacking systematic analysis of their combined effects. Therefore, it is imperative to investigate modified asphalt performance from multiple dimensions—including solid waste type, dosage, and particle size—to provide precise technical guidance for asphalt modification.

To address this gap, this study selected three representative solid waste NMP: industrial nanoscale silica fume, conventional hydrated lime, and cement commonly used in road engineering. Their morphological and pore structure characteristics were analyzed via scanning electron microscopy (SEM) and nitrogen adsorption tests. Modified asphalts were prepared with varying formulations, and their performance was evaluated through dynamic shear frequency tests, multi-stress creep recovery tests (MSCR), bending beam rheometer tests (BBR), and atomic force microscopy (AFM). The study systematically examined the impacts of waste type, dosage, and particle size on both macroscopic rheological properties and nanoscale surface roughness/mechanical behaviors, thereby qualitatively and quantitatively revealing the modification mechanisms of solid waste NWP in asphalt. These findings offer new perspectives for developing sustainable pavement materials.

2. Materials and Methods

2.1. Raw Materials

2.1.1. Asphalt Binder

70# penetration-grade original asphalt was selected, with its basic properties presented in

Table 1. Test results of 70# asphalt performance.

Test Items	Units	Technical Requirements	Test Results
Penetration degree (25 °C)	0.1 mm	60~80	68
Ductility (15 °C)	cm	≮100	>150
Softening point	°C	≮45	47.4
Density (15 °C)	g/cm3	/	1.019
RTFO residue
Mass loss	%	≯±0.8	Qualified
Penetration ratio	%	≮61	70
Ductility after aging (15 °C)	cm	≮15	>100

.

2.1.2. Solid Waste Nano-Micro-Powders

Seven types of solid waste NMP, categorized by type, dosage, and particle size, were selected, with specific parameters detailed in

Table 2. Basic parameters and test scheme of NMP.

Number	Code	Type	Mesh	Content (%)	D5 (μm)	D50 (μm)	D90 (μm)
1	Hydrated lime	HL-P1	200−300	2.5%	15.221	26.156	59.523
2		HL-P1		5.0%
3		HL-P1		7.5%
4		HL-P2	400−500	5.0%	7.156	15.486	42.335
5		HL-P3	800−1000		4.389	6.134	21.336
6	Portland cement	PC-P1	200−300		10.358	29.268	63.123
7	Silica fume	SF-P1	2000−3000		0.396	3.126	6.135

. Among them, the hydrated lime was produced by Chongqing Changpeng Chemical Co., Ltd., located in Chongqing, China. the cement by Zhejiang Sanshi Group Special Cement Co., Ltd., located in Hangzhou, China. and the silica fume by Sichuan Langtian Resources Comprehensive Utilization Co., Ltd., located in Meishan, China.

2.1.3. Preparation of Modified Asphalt

Modified asphalt specimens were fabricated using three categories of solid waste NMP (seven types in total) blended with 70# original asphalt (OR). The dispersion of NMP in asphalt was achieved using a self-developed ultrasonic dispersion instrument (illustrated in Figure 1 and Figure 2). Fluorescence microscopy was employed to capture images of modified asphalt samples prepared under varying parameters. Uniformity assessment of NMP dispersion was conducted to determine optimal preparation parameters, as summarized in

Table 3. Preparation parameters of NMP-modified asphalt.

Number	Type	Mesh	Content (%)	Experimental Conditions
				Temperature (°C)	Time (min)	Speed (r/min)
1	HL-P1	200–300	2.5%	150	40	5000
2	HL-P1		5.0%	150	40	5000
3	HL-P1		7.5%	150	40	5000
4	HL-P2	400–500	5.0%	170	20	5000
5	HL-P3	800–1000		170	20	5000
6	PC-P1	200–300		150	40	5000
7	SF-P1	2000–3000		170	20	5000
8	OR	/	/	/	/	/

.

2.2. Test Methods

2.2.1. Nitrogen Adsorption and Scanning Electron Microscopy (SEM)

The nitrogen adsorption experiment was conducted using a Micromeritics ASAP2460 analyzer at liquid nitrogen temperature (77 K). The device is produced by Micromeritics (Shanghai) Instrument Co., Ltd., located in Shanghai, China. Prior to the experiment, the sample was heated in an oven to remove surface-adsorbed moisture and gaseous contaminants. The pore size distribution was analyzed using the BJH (Barrett-Joiner-Halenda) model based on the desorption branch data. Surface morphology images of NWP were acquired using a Hitachi Regulus 8100 at an accelerating voltage of 20 kV, working distance of 6.3 mm, and beam current of 0.5 nA. The device is provided by Hitachi Scientific Instruments (Beijing) Co., Ltd., located in Beijing, China.

2.2.2. Dynamic Shear Frequency Sweep Test

A TA dynamic shear rheometer was employed to investigate the high-temperature rheological behavior of modified asphalt. Scanning frequencies ranged from 0.1 to 100 rad/s at four temperatures (30 °C, 40 °C, 50 °C, 60 °C) using parallel plate geometry (8 mm diameter, 2 mm gap).

2.2.3. Repeated Multi-Stress Creep Recovery Test (MSCR)

MSCR tests were performed using a DSR at two stress levels (0.1 kPa and 3.2 kPa) and 60 °C. Each stress level involved 10 continuous cycles, with each cycle consisting of 1 s of shear creep loading and 9 s of recovery, totaling 200 s. Performance was evaluated based on non-recoverable creep compliance (J_nr) and creep recovery rate (R). The calculations were performed according to Equations (1)–(3). Stress sensitivity indices were introduced to analyze ${\mathrm{R}}_{\mathrm{D}}$ and ${\mathrm{J}}_{\mathrm{n}\mathrm{r}-\mathrm{D}}$, such as Equations (4) and (5).

$${\gamma }_r(p,N)={\gamma }_r/{\gamma }_p\times 100\%$$

(1)

$$R={\displaystyle \frac{{\sum }_{N=1}^{10}{\gamma }_r(p,N)}{10}}$$

(2)

$$J_{nr}(p,N)={\displaystyle \frac{{\gamma }_u}{P}}$$

(3)

$$R_D={\displaystyle \frac{R\left(0.1\right)-R\left(3.2\right)}{R\left(0.1\right)}}\times 100\%$$

(4)

$$J_{nr-D}={\displaystyle \frac{J_{nr}\left(3.2\right)-J_{nr}\left(0.1\right)}{J_{nr}\left(0.1\right)}}\times 100\%$$

(5)

In the equation, $\gamma$—the recovery rate; ${\gamma }_p$—the maximum strain during the loading cycle; ${\gamma }_r$—the recovery strain during the loading cycle; ${\gamma }_u$—the initial strain during the loading cycle; and P—the applied stress, Pa.

2.2.4. Bending Beam Rheometer (BBR) Test

The BBR test was conducted using a TE-BBR Bending Beam Rheometer. This equipment is provided by Cannon Instrument Company, with production located in State College, PA, United States. Asphalt specimens with dimensions of 127 mm × 12.7 mm × 6.35 mm were tested at −12 °C. The low-temperature performance of modified asphalt was evaluated using creep stiffness (S) and the rate of change in creep stiffness (m-value). Creep stiffness (S) reflects the sensitivity of asphalt to low-temperature conditions and characterizes its low-temperature crack resistance. A higher creep stiffness indicates lower viscous components and higher elastic components in NMP-modified asphalt, resulting in reduced deformation capacity and increased susceptibility to low-temperature fracture. The creep rate (m-value) reflects the rate at which asphalt stiffness changes with loading time. A higher m-value signifies greater low-temperature flexibility and reduced brittleness, thereby lowering the risk of fracture.

2.2.5. Grey Relational Analysis (GRA)

Grey Relational Analysis (GRA), a core component of Grey System Theory proposed by Professor Deng Julong [22], is widely used to evaluate the influence of factors in uncertain systems on reference indicators [23]. This study selected softening point, complex modulus (G*), and creep recovery rate (R) as reference sequences, while density, principal component content, specific surface area (SSA), hydrophilic coefficient, particle size (D₅₀), and pore structure served as comparative sequences. GRA was employed to calculate the correlation degrees between the six comparative sequences and each reference sequence, thereby identifying the key characteristic parameters of NMP that influence asphalt rheological properties.

2.2.6. Atomic Force Microscopy (AFM) Analysis

The AFM experiment was conducted using a Bruker Dimension Icon atomic force microscope equipped with a standard scanner (30 μm × 30 μm × 5 μm). This device is provided by Bruker GmbH, located in Munich, Germany. The XY-axis control resolution reached 16-bit, while the Z-axis achieved 26-bit, meeting the requirements for nanoscale topographic analysis. This instrument operates in four primary modes: Tapping Mode, Contact Mode, Peakforce Mode, and QNM-Young’s Modulus.

The QNM-Young’s Modulus mode, a proprietary technology based on the latest Peakforce Mode, enables simultaneous acquisition of sample topography and multiple mechanical properties. By integrating the Derjaguin-Muller-Toporov (DMT) model with measured force-distance data, quantitative parameters such as modulus, adhesion force, dissipation energy, and deformation can be obtained. The system also generates 3D topographic maps for intuitive visualization and analysis.

The operational principle of QNM is illustrated in Figure 3. The AC curve represents the approach phase of the probe toward the sample: Point A marks the initial position, Point B denotes the contact point where adhesion occurs between the probe and sample, and Point C is the final position. The CE curve corresponds to the retraction phase: Starting from Point C and ending at Point E, with Point D indicating the maximum adhesion event. AFM converts the force-time relationship into force-distance curves between the probe and sample.

The interaction between the probe and sample resembles a metallic object engaging with a viscoelastic material. Adhesion force and Young’s modulus are derived through DMT model fitting, as expressed in Equations (6) and (7).

$$F_t={\displaystyle \frac{4}{3}}E\sqrt{Rd}+F_a$$

(6)

$$E={\left(\left(1-V_s^2\right)/E_s+\left(1-V_t^2\right)/E_t\right)}^{-1}$$

(7)

In the equation, ${\mathrm{F}}_{\mathrm{t}}$—probe-applied force; ${\mathrm{F}}_{\mathrm{a}}$—adhesion force between probe and sample; R—probe tip radius; d—sample deformation; V_S, V_t—poisson’s ratios of the sample and the probe tip; and ${\mathrm{E}}_{\mathrm{s}}$, ${\mathrm{E}}_{\mathrm{t}}$—young’s moduli of the sample and the probe tip.

3. Results and Discussion

3.1. Surface Morphology and Pore Characteristics

Nitrogen adsorption tests and scanning electron microscopy (SEM) were employed to analyze the surface pore structure and particle size of solid waste NMP. The results are presented in Figure 4 and Figure 5.

As shown in Figure 4a–c, for the same type of solid waste NMP, smaller particle sizes correspond to larger pore volumes. This phenomenon is primarily attributed to the increased specific surface area per unit mass with decreasing particle size, which leads to a higher number of surface pores and consequently greater pore volume. Comparing Figure 4a,d, a significant difference in nitrogen adsorption capacity is observed between hydrated lime and cement, despite their similar particle sizes. This discrepancy is mainly related to the forming process of hydrated lime, which results in a loose surface structure with larger open pores. Among the three materials, silica fume exhibits the highest adsorption capacity (Figure 4a–e), owing to its smaller particle size and the largest specific surface area per unit mass.

SEM observations (Figure 5a) reveal that silica fume particles exhibit a loose morphology with numerous surface pores and folded structures, contributing to strong adsorption capacity during interaction with asphalt. In contrast, the particles in Figure 5b display diverse shapes (spherical, blocky, and acicular) with sharp edges and a relatively smooth surface, resulting in the weakest interaction with asphalt. The particles in Figure 5c are predominantly spherical, with a rough surface and a mean particle size of approximately 1 μm. Due to their minimal size and high surface potential energy, these particles demonstrate the strongest adsorption capacity.

3.2. Rheological Properties

To investigate the rheological behavior of solid waste NMP-modified asphalt under varying temperatures and frequencies, the time-temperature superposition principle (TTSP) was applied. Shift factors for each reference temperature were determined by fitting dynamic frequency sweep test results, enabling the horizontal translation of modulus curves obtained at three other temperatures onto a designated reference curve (40 °C). The resulting master curves of complex shear modulus (G*) are presented in Figure 6.

Figure 6a reveals that the G* master curves of original asphalt and hydrated lime-modified asphalt exhibit similar trends: G* increases with frequency, though the growth rate of original asphalt significantly decelerates at high frequencies, whereas hydrated lime-modified asphalt maintains a robust upward trend. Under identical loading frequencies, higher NMP content correlates with elevated G*, but the marginal increase diminishes progressively. Notably, the modulus enhancement at 2.5% dosage is substantially greater than at 5% or 7.5%, as evidenced by the narrowing gap between master curves with increasing dosage.

Figure 6b demonstrates that the modulus–frequency relationships of NMP-modified asphalts with three distinct particle sizes follow comparable patterns, with G* rising steadily as frequency increases. At constant frequency, finer particles yield higher moduli due to their greater specific surface area per unit mass, which enhances adsorption of light asphalt components when equivalent mass dosages are applied.

Figure 6c shows that the G* master curves of asphalts modified with hydrated lime, silica fume, and cement exhibit analogous frequency-dependent behavior, with G* increasing monotonically. At the same frequency, silica fume-modified asphalt displays the highest G*, followed by hydrated lime and cement, primarily attributable to differences in particle size. However, the spacing between master curves varies significantly: silica fume-modified asphalt shows markedly wider separation compared to hydrated lime and cement, indicating stronger modulus enhancement at equivalent dosages, particularly pronounced at low frequencies.

3.3. High-Temperature Performance

Based on the Multiple Stress Creep Recovery (MSCR) test results, the recovery ratio (R), non-recoverable creep compliance (J_nr), stress sensitivity indices for recovery ratio (R_D), and stress sensitivity of unrecoverable creep compliance (J_nr-D) were calculated and presented in

Table 4. MSCR test evaluation index results.

Type	Code	Dosage (%)	0.1 kpa		3.2 kpa		${\mathit{R}}_{\mathit{D}}$	${\mathit{J}}_{\mathit{n}\mathit{r}-\mathit{D}}$
			$\mathit{R}$	Jnr	$\mathit{R}$	Jnr
Original asphalt	OR	/	4.20%	3.39	0.12%	5.87	97.14%	73.16%
Hydrated lime	HL-P1	2.5	25.30%	1.18	0.88%	1.89	96.52%	60.17%
		5	29.30%	0.95	1.59%	1.36	94.57%	43.16%
		7.5	33.20%	0.85	1.89%	1.15	94.31%	35.29%
	HL-P2	5	32.50%	0.78	2.23%	1.01	93.14%	29.49%
	HL-P3		35.20%	0.61	3.39%	0.76	90.37%	24.59%
Portland cement	PC-P1		15.80%	1.29	0.45%	2.11	97.15%	63.57%
Silica fume	SF-P1		35.20%	0.52	3.85%	0.62	89.06%	19.23%

. The data indicate that the deformation recovery capacity of NMP-modified asphalt significantly surpasses that of original asphalt. For hydrated lime-modified asphalt, increasing dosage and reducing particle size result in a proportional rise in R and an inverse decrease in J_nr, demonstrating enhanced elasticity and rutting resistance with higher dosages. However, under high-stress loading conditions, J_nr increases, indicating greater susceptibility to permanent deformation (rutting).

Additionally, ${\mathrm{R}}_{\mathrm{D}}$ and ${\mathrm{J}}_{\mathrm{n}\mathrm{r}-\mathrm{D}}$ were calculated using Equations (1) and (2). The results reveal that original asphalt exhibits the highest stress sensitivity, which progressively diminishes with increasing micropowder dosage and decreasing particle size. Among the three materials tested, silica fume demonstrates the lowest stress sensitivity. These findings confirm that both reduced particle size and higher NMP dosage enhance the high-temperature performance of asphalt by improving its rutting resistance.

3.4. Low-Temperature Performance

The stiffness (S) and m-value of micropowder-modified asphalt under a 60 s loading at −12 °C are illustrated in Figure 7. Using hydrated lime as an example, both S increases and the m-value decreases with higher dosages and smaller particle sizes. Among the three NMP types, silica fume exhibits the highest S, while cement shows the greatest m-value. These trends indicate that NMP modification adversely affects low-temperature performance, as the incorporation of NMP primarily enhances toughness by increasing elastic components while reducing viscous fractions. This results in improved high-temperature stability but elevated low-temperature stiffness, rendering the asphalt more prone to brittle fracture under cold conditions.

To further analyze flexural deformation behavior, the Burgers model was employed for parameter fitting based on Bending Beam Rheometer (BBR) test data [24]. The model comprises Maxwell and Kelvin elements connected in series with four total components [25], as shown in Figure 8.

The constitutive Equation for the Burgers model is given in Equation (8).

$$\mathsf{\sigma }+{\mathrm{p}}_1\dot{\mathsf{\sigma }}+{\mathrm{p}}_2\ddot{\mathsf{\sigma }}={\mathrm{q}}_1\dot{\mathsf{\epsilon }}+{\mathrm{q}}_2\ddot{\mathsf{\sigma }},$$

(8)

In the Equation, ${\mathrm{p}}_1={\mathsf{\eta }}_1/{\mathrm{E}}_1+\left({\mathsf{\eta }}_1+{\mathsf{\eta }}_2\right)/{\mathrm{E}}_1$; ${\mathrm{p}}_2={\mathsf{\eta }}_1{\mathsf{\eta }}_2/\left({\mathrm{E}}_1{\mathrm{E}}_2\right)$; ${\mathrm{q}}_1={\mathsf{\eta }}_1$; ${\mathrm{q}}_2={\mathsf{\eta }}_1{\mathsf{\eta }}_1/{\mathrm{E}}_2$; ${\mathrm{q}}_2={\mathsf{\eta }}_1{\mathsf{\eta }}_1/{\mathrm{E}}_2$; and ${\mathrm{E}}_1$, ${\mathrm{E}}_2$, ${\mathsf{\eta }}_1$, ${\mathsf{\eta }}_2$—the viscoelastic parameters of the model.

Substituting these viscoelastic parameters into Equation (8) yields commonly used Expression (9):

$$E_1{E}_2\mathsf{\sigma }+\left({\eta }_1{E}_1+{\eta }_1{E}_2+{\eta }_2{E}_1\right)\dot{ \sigma }+{\eta }_1{\eta }_2\ddot{\sigma }=E_1{E}_2{\eta }_1\dot{\epsilon }+E_1{E}_1{\eta }_2\ddot{\sigma },$$

(9)

Subsequently, by substituting J$\mathsf{\sigma }=∆\left(\mathrm{t}\right)·{\mathsf{\sigma }}_0$ into commonly used viscoelastic Equation (9) and performing logical derivations, creep Equation (10) for the Burgers model can be obtained.

$$J\left(t\right)={\displaystyle \frac{1}{E_1}}+{\displaystyle \frac{1}{{\eta }_1}}t+{\displaystyle \frac{1}{E_2}}\left(1+e^{{\displaystyle \frac{-E_2}{{\eta }_2}}t}\right),$$

(10)

In the equation, $\mathrm{J}\left(\mathrm{t}\right)$—the creep compliance of the model, $\mathrm{J}\left(\mathrm{t}\right)=\mathsf{\epsilon }\left(\mathrm{t}\right)/{\mathsf{\sigma }}_0$, $\mathsf{\epsilon }\left(\mathrm{t}\right)=3\mathrm{F}\mathrm{L}/2\mathrm{b}{\mathrm{h}}^2$, ${\mathsf{\sigma }}_0=6\mathrm{h}\mathrm{u}\left(\mathrm{t}\right)/{\mathrm{L}}^2$; $\mathrm{u}\left(\mathrm{t}\right)$—the mid-span deflection; L—the specimen span length; h—the beam height of the specimen; b—the specimen width; t—time; and ${\mathrm{E}}_1$, ${\mathrm{E}}_2$, ${\mathsf{\eta }}_1$, ${\mathsf{\eta }}_2$—model parameters, where ${\mathsf{\eta }}_1$ is the viscous parameter, ${\mathsf{\eta }}_2$ is the delayed viscous parameter,${\mathrm{E}}_1$ is the instantaneous elastic parameter, ${\mathrm{E}}_2$ is the instantaneous elastic parameter.

Therefore, nonlinear curve fitting of the Burgers model was performed using 1st Opt software, yielding four viscoelastic parameters (${\mathrm{E}}_1$, ${\mathrm{E}}_2$, ${\mathsf{\eta }}_1$, ${\mathsf{\eta }}_2$) and calculating the relaxation times ($\mathsf{\lambda }={\mathsf{\eta }}_1/{\mathrm{E}}_1$), as summarized in

Table 5. List of Burgers model data parameters.

Type	Content (%)	${\mathit{E}}_1$ (MPa)	${\mathit{E}}_2$ (MPa)	${\mathit{\eta }}_1$ (MPa·s)	${\mathit{\eta }}_2$ (MPa·s)	$\mathit{\lambda }$	R2
OR	/	661.25	399.45	58,072.18	11,945.33	87.85	0.999
HL-P1	2.5	726.15	592.33	69,259.69	23,562.15	95.38	0.992
	5.0	885.45	669.87	88,593.52	31,536.25	100.05	0.996
	7.5	936.58	745.22	105,515.12	41,879.22	112.66	0.995
HL-P2	5.0	1145.78	938.78	152,834.84	138,596.15	133.39	0.989
HL-P3		1378.29	1239.16	192,489.33	399,263.45	139.66	0.993
PC-P1		688.33	428.33	65,214.26	12,656.33	94.74	0.999
SF-P1		1525.44	1553.15	223,645.22	524,536.55	146.61	0.991

. The software version is 2.5, developed by 7D-Soft High Technology Inc., which is located in Beijing, China.

Fitted Burgers model parameters for NMP-modified asphalt are presented in Table 5. The viscous parameters (${\mathsf{\eta }}_1$, ${\mathsf{\eta }}_2$) dominate over the elastic moduli (${\mathrm{E}}_1$, ${\mathrm{E}}_2$), with ${\mathsf{\eta }}_1$ and ${\mathsf{\eta }}_2$ exceeding ${\mathrm{E}}_1$ and ${\mathrm{E}}_2$ by at least two orders of magnitude, confirming the predominantly viscous nature of the asphalt materials. Among the four parameters, ${\mathsf{\eta }}_1$ (characterizing viscous behavior) correlates with deformation resistance: higher ${\mathsf{\eta }}_1$ values indicate stronger anti-deformation capacity, which improves with increasing NMP dosage and decreasing particle size.

The relaxation parameter ($\mathsf{\lambda }$) reflects the material’s ability to dissipate applied stress over time, with smaller $\mathsf{\lambda }$ values indicating faster stress relaxation and reduced low-temperature cracking susceptibility. As shown in Table 5, NMP incorporation significantly increases $\mathsf{\lambda }$, implying impaired stress dissipation. For hydrated lime-modified asphalt, higher dosages correlate with prolonged relaxation times, attributed to increased adsorption of free asphalt onto microparticle surfaces, which reduces fluidity and promotes stress concentration. Additionally, smaller particle sizes further elevate $\mathsf{\lambda }$ due to enhanced surface adsorption capacity, requiring greater energy for stress relaxation and slowing dissipation rates.

3.5. Grey Relational Analysis

This study investigated the performance of asphalt modified with the same type of mineral powder at varying particle sizes and dosages, revealing that both dosage and particle size significantly influence asphalt properties. However, upon analyzing their intrinsic relationships, it was found that differences in dosage and particle size could be characterized by variations in the total surface area incorporated into the asphalt, leading to differences in the amount of free asphalt adsorbed by the mineral powder and, consequently, variations in asphalt performance. Although performance studies were also conducted on different types of mineral powders, their properties are influenced by multiple factors, including density, particle size, specific surface area (SSA), hydrophilic coefficient, composition, and pore structure. To clarify the extent to which these properties of three NMP affect asphalt performance, grey relational analysis (GRA) was employed in this study.

The analysis calculated the relational degrees between the properties of NMP (density, particle size (D₅₀), SSA, hydrophilic coefficient, major component content, and pore structure) and asphalt performance metrics (softening point, G*, and R), thereby identifying key characteristic parameters influencing asphalt performance.

Using the softening point, G*, and R as reference sequences, and NMP density, oxide component content, SSA, hydrophilic coefficient, D₅₀, and pore structure as comparative sequences, the relational degrees of the six comparative sequences relative to each reference sequence were calculated. The results for the softening point are presented in

Table 6. Calculation Results of Grey Correlation Coefficient.

Comparative Sequences	GRA			Grey Correlation Degree
	PC-P1	HL-P1	SF-P1
Density (g/cm3)	1.00	0.42	0.33	0.584
major component content (%)	0.40	1.00	0.33	0.576
SSA (m2/g)	1.00	0.92	0.33	0.752
hydrophilic coefficient	0.64	0.33	1.00	0.657
particle size (μm)	0.33	0.81	1.00	0.716
pore structure	1.00	0.33	0.38	0.572

. According to the table, the ranking of the six characteristics’ relational degrees with the softening point, from highest to lowest, is as follows: SSA > D₅₀ > hydrophilic coefficient > density > major component content > pore structure. Similar calculations for the complex modulus and creep recovery rate yielded the following rankings: SSA > D₅₀ > pore structure > major component content > density > hydrophilic coefficient.

The softening point and G* characterize the high-temperature stability of asphalt, while the R reflects its recovery ability during deformation. Based on the grey relational degrees, the SSA of different NMP types at the same dosage exerts the greatest influence on the high-temperature and viscoelastic properties of asphalt. This finding aligns with the preceding analysis in this study: NMP with larger specific surface areas more readily adsorb light oil fractions in asphalt, enhancing the prominence of medium-to-large molecular asphaltenes and resulting in modified asphalt with superior deformation resistance.

3.6. Nano-Mechanical Properties

3.6.1. Surface Adhesion Force Analysis

Adhesion force values of solid waste mineral powder-modified asphalt were obtained using Atomic Force Microscopy (AFM) based on the imaging principles of Quantitative Nanomechanical (QNM) technology, as shown in

Table 7. Surface adhesion of NMP-modified asphalt.

Type	OR	PC-P1	HL-P1	HL-P1	HL-P1	HL-P2	HL-P3	SF-P1
Content	/	5%	2.5%	5.0%	7.5%	5.0%
Fa(max) (nN)	9.9	10.7	11.5	11.4	11.9	12.5	12.5	12.7
Fa(min) (nN)	4	4.4	5.7	6.5	6.9	7.6	8.1	8.5

.

The following patterns were identified from the data. (1) After incorporating solid waste NMP into original asphalt, all three types improved the adhesion force, with the following order of effectiveness: SF > HL > PC. However, significant differences were observed in their effects on maximum and minimum adhesion forces. Silica fume exhibited the most pronounced improvement, increasing the maximum adhesion force F_a(max) by 28% and the minimum adhesion force F_a(min) by 112% compared to original asphalt. The reduced range between F_a(max) and F_a(min) indicates that silica fume homogenized adhesion forces across different asphalt regions, significantly enhancing overall adhesion performance. (2) For hydrated lime, varying dosages had minimal impact on F_a(max), with a 4% increase observed when the dosage increased from 2.5% to 7.5%. In contrast, F_a(min) showed a more pronounced response, improving by approximately 21% under the same dosage increase. (3) No clear correlation was found between hydrated lime particle size and F_a(max). However, F_a(min) exhibited an inverse relationship with particle size—smaller particles yielded higher F_a(min). For instance, HL-P3 (finer particles) increased F_a(min) by 25% compared to HL-P1 (coarser particles), thereby reducing the adhesion force range.

The data analysis reveals that solid waste mineral powders primarily improve adhesion by increasing F_a(min), which narrows the gap between maximum and minimum adhesion forces.

3.6.2. Surface Modulus Analysis

Figure 9 presents the Derjaguin–Müller–Toporov (DMT) modulus (surface mechanical modulus) of solid waste NMP-modified asphalt obtained via AFM testing. In the modulus maps, purple regions indicate higher modulus values, while red regions represent lower modulus values. Comparative analysis of modulus maps and numerical data for different NMP-modified asphalts revealed the following.

(1) The addition of PC and HL to original asphalt resulted in a significant increase in discrete purple peaks. In contrast, SF modification led to the disappearance of isolated purple peaks and the formation of extensive contiguous purple areas, where originally separated peaks coalesced, accompanied by a abrupt increase in modulus. (2) For HL-modified asphalt at three different dosages, the modulus increased proportionally with dosage. However, the modulus maps showed only an increase in the number of isolated purple peaks without extensive peak coalescence as dosage increased. (3) When comparing HL-modified asphalts with varying particle sizes, smaller particle sizes correlated with greater modulus enhancement. The modulus maps exhibited larger contiguous areas of coalesced peaks for finer HL particles, leading to an overall increase in the modified asphalt’s modulus.

3.6.3. Surface Roughness Analysis

Height sensor phase maps obtained under Quantitative Nanomechanical (QNM) mode were processed using the Roughness module in NanoScope Analysis software to directly extract two key roughness parameters: maximum-to-minimum height difference (R_max) and image surface area difference (ISAD)—the latter representing the percentage difference between the flattened surface area (projected onto the X-Y plane) and the actual rugged surface area of the scanned region (Figure 10). The software version is 1.5, provided by Bruker (Germany), with its headquarters located in Munich, Germany. Roughness parameters for original asphalt and NMP-modified asphalts were calculated and presented in

Table 8. Statistical Table of Surface Roughness of NMP-Modified Asphalt.

Code	Rmax (nm)	ISAD (%)
OR	58.9	0.0326
PC-P1-5.0%	55.9	0.0389
HL-P1-2.5%	56.1	0.0405
HL-P1-5.0%	55.3	0.0424
HL-P1-7.5%	56.2	0.0411
HL-P2-5.0%	30.2	0.0488
HL-P3-5.0%	29.5	0.0635
SF-P1-5.0%	24.6	0.0924

.

The data reveal that R_max decreased after mineral powder incorporation, with SF (exhibiting the strongest adsorption capacity) reducing R_max by over 50%. ISAD increased with both higher dosage and smaller particle size of the NMP. This trend correlates closely with compositional changes induced by powder adsorption, as discussed earlier.

Mechanistically, NMP primarily adsorbs saturated fractions from the asphalt surface, which typically occupy depressions with lower elevation profiles. Upon adsorption, the minimum surface heights increase, thereby reducing R_max. Notably, SE and fine-particle HL—due to their superior adsorption capacity and higher particle count per unit mass—not only adsorb saturated fractions but also aromatic fractions, reducing their relative content while increasing asphaltene and resin proportions. This compositional shift manifests as increased surface roughness, with originally smooth regions becoming rugged, which in turn elevates ISAD values.

4. Conclusions

(1) Morphological and pore structure analysis via SEM and BET nitrogen adsorption tests revealed that PC particles exhibited diverse morphologies with relatively smooth surfaces. HL displayed a porous, loosely structured surface. SF comprised spherical particles with rough surfaces and the smallest particle size. Among the tested powders, SF and HL exhibited the highest pore volumes, while PC showed the lowest. Additionally, for the same powder type, smaller particle sizes correlated with increased surface porosity.

(2) Rheological property analysis of modified asphalts demonstrated consistent trends in G* with increasing frequency. At identical frequencies and dosages, SF-modified asphalt exhibited the highest G*, followed by HL and PC. For the same material and frequency, G* increased with both decreasing particle size and increasing dosage, with particle size exerting a more pronounced effect.

(3) MSCR test results indicated that ${\mathrm{R}}_{\mathrm{D}}$ and ${\mathrm{J}}_{\mathrm{n}\mathrm{r}-\mathrm{D}}$ decreased with increasing powder dosage. Stress sensitivity further diminished with decreasing particle size (increased SSA). Among the three powders, silica fume (smallest particle size/highest specific surface area) demonstrated the lowest stress sensitivity values (89.06% for ${\mathrm{R}}_{\mathrm{D}}$ and 19.23 kPa⁻¹ for ${\mathrm{J}}_{\mathrm{n}\mathrm{r}-\mathrm{D}}$), indicating superior high-temperature deformation resistance.

(4) Low-temperature performance tests revealed an inverse correlation between m-value and particle size, while m-value showed positive correlations with dosage and SSA. This suggests adverse effects of NMP on low-temperature properties. The relaxation time (λ) obtained from the Burgers model exhibited identical trends to m-value, confirming the model’s applicability for analyzing low-temperature behavior of NMP-modified asphalts.

(5) Grey relational analysis identified SSA as the most influential parameter affecting asphalt performance, with the highest correlations to softening point, G*, and R. This confirms SSA as the characteristic indicator for NMP impact on asphalt performance across temperature ranges, supporting a predominantly physical adsorption modification mechanism.

(6) The improvement of adhesion force of solid waste NMP at the nano-scale is mainly achieved by increasing its F_a(min), thereby reducing the range between the maximum and minimum values. Increased surface modulus via adsorption of light fractions (saturated components) was observed, thereby elevating the relative content of heavy fractions (asphaltene and resin).

5. Patents

This paper has generated two patents:

(1)

Patent name: An asphalt feeding and mixing device, Authorization Announcement Number: CN 114214084 B.

(2)

Patent name: A method of adding powder particles to asphalt, Authorization Announcement Number: CN 114214083 B.