Cross-Scale Characterization of Fatigue Damage in Warm-Mix Asphalt Based on Linear Amplitude Sweep and Four-Point Bending Tests

Summary

This study establishes a robust cross-scale framework linking binder damage mechanics to mixture fatigue performance, demonstrating that linear amplitude sweep–simplified viscoelastic continuum damage (LAS–S-VECD) parameters provide a reliable, mechanistically grounded basis for predicting and designing durable warm-mix asphalt systems.

Abstract

Fatigue cracking is a critical factor governing the long-term durability of asphalt pavements, while the cross-scale relationship between binder fatigue behavior and mixture fatigue performance remains insufficiently understood for warm-mix asphalt (WMA). In this study, the fatigue characteristics of WMA were systematically investigated at both binder and mixture scales to establish quantitative cross-scale correlations. Dynamic shear rheometer (DSR) tests and linear amplitude sweep (LAS) tests interpreted using the simplified viscoelastic continuum damage (S-VECD) framework were employed to characterize the rheological properties and damage evolution of asphalt binders with different crude oil origins. Mixture-scale fatigue performance was evaluated using strain-controlled four-point bending fatigue tests. The results indicate that aging significantly increases binder stiffness and accelerates fatigue degradation, with the fatigue factor G*·sin δ increasing by approximately 150–250% after long-term aging. The effectiveness of warm-mix modification at the binder scale was strongly binder-dependent, as reflected by an 8–13% reduction in the damage rate coefficient for Binders A and B but an approximately 11% increase for Binder C. Conventional rheological indicators such as sin δ exhibited limited and material-dependent capability in predicting mixture fatigue life, whereas LAS–S-VECD-derived damage parameters showed consistently strong correlations with mixture-scale fatigue performance. Overall, this study demonstrates that LAS–S-VECD-based binder damage characterization provides a robust basis for predicting mixture fatigue resistance and supports its application in performance-based mixture design for durable and sustainable WMA pavements.

Introduction

Conventional asphalt pavement construction relies on high-temperature processing, typically ranging from 160 °C to 180 °C, and exceeding 190 °C for modified binders such as rubberized asphalt and high-performance polymer-modified bitumen. In specialized applications, including steel bridge deck pavements, in-situ mixture placement temperatures may surpass 200 °C¹. These extreme thermal conditions result in substantial fossil fuel consumption and generate significant atmospheric emissions, including greenhouse gases and hazardous asphalt fumes rich in benzene-soluble compounds and carcinogenic polycyclic aromatic hydrocarbons (e.g., benzo[a]pyrene)^2,3. Previous studies have consistently shown that reducing asphalt production and compaction temperatures can lower fuel consumption, CO₂ emissions, and occupational exposure to asphalt fumes, although the magnitude of these benefits depends on mixture type, plant configuration, additive dosage, and field construction conditions. Recent studies have further enriched the understanding of asphalt performance under various modifications and service conditions. It has been reported that the introduction of calcium lignosulfonate into asphalt mixtures can effectively delay thermo-oxidative aging by inhibiting oxidation reactions and stabilizing the colloidal structure of asphalt binders.

In terms of fracture behavior, investigations of hot mix asphalt (HMA) and warm mix asphalt (WMA) under pure Mode I and Mode II loading conditions have demonstrated that loading mode plays a critical role in governing low-temperature fracture toughness and energy dissipation. Moisture susceptibility has also been extensively studied in rubber-modified asphalt systems, where recycled rubber materials improve resistance to moisture-induced damage, and optimal rubber content can be determined through combined mechanical and economic evaluation approaches. Regarding high-temperature performance, modified stone matrix asphalt (SMA) has been evaluated using Dynamic Creep and Hamburg Wheel Tracking Device tests, confirming that the mixture modification significantly enhances rutting resistance. In addition, semicircular bending (SCB)-based studies on asphalt mixtures incorporating recycled additives have shown notable improvements in Mode I fracture resistance and moisture damage resistance, highlighting the synergistic effects of recycled materials on fatigue and durability performance. Consequently, the development of low-temperature asphalt technologies has emerged as a critical pathway toward sustainable pavement construction and environmentally responsible infrastructure systems.

Warm mix asphalt (WMA) technology, achieved through the incorporation of chemical additives, organic waxes, or foaming techniques, enables effective mixture production at temperatures typically between 90 °C and 130 °C—representing a reduction of 30–50 °C compared with conventional hot mix asphalt (HMA)⁴. Beyond its well-documented benefits in reducing energy demand and pollutant emissions, WMA plays a pivotal role in mitigating the thermo-oxidative aging of asphalt binders during production and placement. Asphalt aging is governed by temperature-dependent chemical kinetics, with oxidation rates approximately doubling for every 10 °C increase in temperature^5,6. Elevated temperatures accelerate volatilization, oxidation, and polymerization reactions, progressively transforming maltenes into rigid asphaltenes and thereby increasing binder stiffness while reducing ductility⁷. By lowering production temperatures, WMA suppresses these deleterious reactions, preserving binder viscoelasticity and potentially enhancing long-term fatigue resistance⁸.

Although the environmental and constructability advantages of WMA have been extensively reported, systematic investigations into its fatigue performance under aging conditions remain comparatively limited. In particular, asphalt binders derived from different crude oil sources—such as Karamay, offshore CNOOC, and CNPC feedstocks—exhibit pronounced variations in chemical composition, including asphaltene content, resin distribution, aromatic fractions, and saturate levels⁹. These compositional differences are widely recognized as fundamental determinants of rheological behavior, aging susceptibility, and fatigue durability¹⁰. Nevertheless, existing fatigue studies seldom differentiate binders based on crude oil origin, resulting in an incomplete understanding of how source-dependent chemistry governs fatigue performance, especially under cumulative aging representative of in-service conditions^11,12. From an engineering perspective, a reliable binder-scale fatigue evaluation method would be particularly useful for preliminary material screening, warm-mix additive selection, aging sensitivity assessment, and quality control before mixture-level verification. Nevertheless, LAS–S-VECD should not be regarded as a complete substitute for mixture fatigue testing because aggregate gradation, air voids, binder–aggregate interaction, compaction quality, and field aging may also govern pavement fatigue performance. Furthermore, the relationship between binder-scale fatigue indicators and mixture-scale fatigue behavior has not been conclusively established across diverse asphalt sources¹³. While rheological tests such as the Linear Amplitude Sweep (LAS) have shown promise in characterizing binder fatigue damage, their predictive reliability for mixture fatigue life—particularly for binders with distinct chemical origins—remains insufficiently validated¹⁴. This disconnect limits the accuracy of laboratory-based performance predictions and constrains rational material selection for engineering practice¹⁵.

To address these critical gaps, this study conducts a comprehensive, multi-scale investigation into the fatigue behavior of warm-mix modified asphalt binders derived from three distinct crude oil sources¹⁶. By integrating dynamic shear rheometer (DSR) analysis, Linear Amplitude Sweep (LAS) testing within the Simplified Viscoelastic Continuum Damage (S-VECD) framework, and mixture-scale four-point bending fatigue tests, this work systematically evaluates the influence of crude oil origin, warm-mix modification, and aging on fatigue resistance^17,18,19. The findings aim to establish robust cross-scale correlations between binder rheology and mixture performance, providing a mechanistic basis for fatigue life prediction and offering practical guidance for the design and selection of sustainable asphalt materials.

This study presents a cross-scale fatigue characterization framework for warm-mix asphalt by integrating binder-scale LAS–S-VECD analysis with mixture-scale four-point bending fatigue testing. Compared with previous studies that mainly focus on either binder-level rheological evaluation or mixture-level performance assessment in isolation, the present work establishes a direct mechanistic linkage between crude oil–dependent binder chemistry, warm-mix modification, and mixture fatigue behavior under aging conditions. The novelty of this study lies in three aspects: (i) explicit incorporation of crude oil origin as a governing variable for fatigue performance; (ii) systematic cross-scale correlation between LAS–S-VECD damage evolution and mixture fatigue life; and (iii) unified evaluation of warm-mix modification effects across binder and mixture scales. The results demonstrate that LAS–S-VECD-derived damage parameters provide robust predictors of mixture fatigue performance, offering a more mechanistically grounded alternative to conventional rheological indices. These findings establish a scientific basis for performance-oriented evaluation and design of sustainable warm-mix asphalt systems.

Protocol

Materials
The three asphalt binders selected in this study, as summarized in Table 1, are representative pavement binders derived from different crude oil sources and have been widely used in practical road engineering in China. Karamay asphalt, CNOOC 36-1 asphalt, and PetroChina asphalt differ markedly in crude origin, chemical composition, aging susceptibility, and rheological characteristics, providing a suitable material basis for investigating oil-source-dependent fatigue behavior. Their selection enables a comparative evaluation of how intrinsic binder composition influences the effectiveness of warm-mix modification and mixture-scale fatigue performance, thereby enhancing the engineering relevance of the proposed cross-scale fatigue characterization framework. Detailed geological origins and chemical characteristics of each binder are as follows:

Binder A: Derived from heavy oil feedstock of the 9th zone, produced via a blending process of vacuum residue and deoiled asphalt. Its base material exhibits distinctive properties, including low paraffin content (<2%), minimal sulfur concentration, and high resin composition. Notably, Karamay asphalt is the only pavement binder with a specific gravity below 1 g/cm³ in current engineering applications, and it features superior dynamic viscosity and excellent ductility retention after aging. These characteristics make it particularly suitable for regions subjected to large diurnal temperature variations and intense ultraviolet exposure.

Binder B: Originates from the rare heavy crude oil extracted from the Suizhong 36-1 offshore oilfield, with a high bitumen yield of 56% through refining. The feedstock is classified as a sulfur-deficient, naphthenic-base heavy crude with a high acid value, resulting in a processed binder with high density (1.012 g/cm³), low paraffin content (1.8%), and elevated resin proportions. Such properties endow the binder with excellent low-temperature flexibility, rendering it advantageous for cold environment applications.

Binder C: Primarily formulated using Venezuelan Boscan heavy crude as the base feedstock, achieving a 60% production yield via specialized refining processes. This crude oil exhibits unique geochemical features, including high acid content, significant heavy metal concentrations, and strong carbon residue formation potential. The binder displays an atypical hydrocarbon composition, characterized by low saturated hydrocarbon fractions, enriched resin-asphaltene complexes, and remarkably low paraffin content (1.3%).

In this investigation, the three base asphalt binders were designated as AO (Karamay), BO (CNOOC 36-1), and CO (PetroChina). Corresponding WMA binders were prepared by incorporating Evotherm M1 additive, coded as AP, BP, and CP, respectively²⁰. Comprehensive performance indices, including penetration, softening point, and ductility, were tested in accordance with JTG E20-2011²¹ specifications, with detailed comparative data presented in Table 1. All experimental procedures were strictly followed by the standardized protocols outlined in the Technical Specifications for Highway Engineering Asphalt and Bituminous Mixtures.

Project	Unit	Karamay	CNOOC	CNPC
Penetration	0.1 mm (15 °C)	22	22	24
	0.1 mm (25 °C)	72	68	71
	0.1 mm (30 °C)	112	110	116
PI	－	-1.14	-1.2	-0.81
TR&B	°C	46	46.5	47.5
Dynamic viscosity (60 °C)	Pa·s	223.5	230	256.9
Ductility (10 °C,5 cm/min)	cm	>100	>100	52
Wax content	%	1.9	1.8	1.3
Flash point (COC)	℃	278	287	312
Solubility	%	99.5	99.7	99.8
Density (15 °C)	g/cm³	0.977	1.012	1.049
RTFOT	Quality change (%)	0.05	0.06	-0.07
	Residual penetration ratio (%)	66.2	67.4	64.8
	Residual ductility (10 °C,cm)	13	12	9

Table 1: Key technical parameters of bituminous binders. Table 1 summarizes the key technical parameters of bituminous binders, including physical properties, temperature susceptibility, rheological characteristics, and short-term aging performance, to evaluate their fundamental properties and durability.

The WMA preparation process involved a strictly controlled multi-stage protocol designed to ensure reproducibility of binder modification. The base asphalt binder was first heated in a forced-convection oven at 135 ± 2 °C for 60 min to achieve a stable molten state, followed by 30 min of equilibration to eliminate thermal gradients. All heating processes were conducted under sealed containers with nitrogen protection (flow rate: 0.5 L/min) to minimize oxidative aging during temperature conditioning.

The Evotherm M1 additive was then incorporated at 135 ± 2 °C under continuous mechanical stirring at 300 rpm for 5 min prior to high-shear processing, ensuring initial dispersion of the surfactant phase. Subsequently, high-shear mixing was performed using a rotor–stator homogenizer at 3000 rpm for 25 min, while maintaining the binder temperature within 135–140 °C using an external oil bath temperature control system (±1 °C accuracy). During the entire mixing process, the temperature was continuously monitored using a calibrated K-type thermocouple inserted into the binder matrix, and fluctuations exceeding ±2 °C triggered automatic heating adjustment. The modified binder was then subjected to a controlled cooling procedure to 25 °C at 5 °C/min before subsequent testing or short-term storage. The shear protocol design followed the viscosity–temperature relationship of asphalt binders, ensuring that all samples were prepared under comparable shear history conditions. This strict thermal–mechanical control guarantees high repeatability and minimizes variability in WMA binder preparation.

Dynamic shear rheometer (DSR) testing
To characterize the rheological response and fatigue-related properties of asphalt binders modified with warm-mix additives, Dynamic shear rheometer (DSR) tests were conducted using a temperature-controlled rotational rheometer in accordance with ASTM D7175²². The rheological evaluation focused on intermediate-temperature fatigue behavior, which is closely associated with crack initiation and propagation in asphalt pavements.

The fatigue factor G*sin δ²³, widely recognized as an indicator of fatigue susceptibility at the binder level, was adopted to quantify changes in viscoelastic dissipation behavior induced by warm-mix modification and aging. Temperature sweep tests were performed over a range of 58–82 °C, with temperature increments of 6 °C. At each target temperature, specimens were allowed to equilibrate for 10 min before data acquisition to ensure thermal stability. To investigate the influence of aging on rheological properties, binder specimens were subjected to three aging conditions: unaged, rolling thin film oven test (RTFOT) aging, and combined RTFOT and Pressure Aging Vessel (PAV) aging ²⁴. These aging protocols were designed to simulate short-term aging during production and placement, as well as long-term aging during in-service pavement operation. The evolution of G*sin δ with temperature and aging condition was analyzed to assess the fatigue resistance of different binders.

Before each DSR test, the binder specimen was carefully trimmed after loading between the parallel plates to ensure a uniform edge profile. The specimen was conditioned at the target temperature for 10 min before measurement. Testing was performed over 58–82 °C at 6 °C increments. A valid test was confirmed when the measured torque and displacement remained within the instrument’s recommended operating range, and no visible specimen slippage occurred.

Linear amplitude sweep (LAS) testing
Viscoelastic behavior characterization was conducted in accordance with ASTM D7175 specifications for dynamic mechanical analysis²⁵. The experimental methodology included strain amplitude sweeps to establish linear viscoelastic boundaries, followed by frequency-controlled testing at 10 rad/s²⁶. Temperature-dependent evaluations covered the operational temperature spectrum of asphalt pavements (58–82°C), executed in 6°C increments with 10 minutes allowed for thermal equilibrium at each isothermal segment. The AASHTO T391 protocol was employed to quantify binder damage accumulation through dissipated energy evolution, specifically monitoring the viscoelastic dissipation factor (|G*|sin δ) during cyclic loading ^27,28. The Simplified Viscoelastic Continuum Damage (S-VECD) framework was adopted to predict degradation patterns of bituminous composites²⁹. The LAS protocol executes an oscillatory amplitude sweep at a fixed 10 Hz frequency, applying controlled strain progression from 0.1% to 30% with 0.1% resolution increments.

Key viscoelastic parameters were derived using the following equations:

log G "(ω) = m (log ω) + b (1)

G'(ω) = G* (ω) × cosδ (ω) (2)

(3)

where G''(ω) is the loss modulus, ω is the angular frequency, m and b are fitting coefficients, G'(ω) is the storage modulus, G*(ω) is the complex modulus, δ(ω) is the phase angle, and is the viscoelasticity index.

Damage quantification employed the fundamental relationship expressed in Equation (4):

(4)

In the formula: C(t)—the integrity parameter, C(t)=G^* (t)/G^* (Initial), G^*- complex modulus (MPa);

γ_0—Applying strain (%);
t—Test duration (s)

The temporal evolution of damage metric D(t) and structural integrity coefficient C(t) is mathematically parameterized through a power-law constitutive relationship (Yuan 2024):

C(t) = C₀ - C₁ × D^C₂ (5)

In the formula: C0​ represents the initial integrity parameter (normally equal to 1) ,C1, C2—fitting parameters.

Calculate the fatigue damage value using the concept of the shear stress peak point:

(6)

Cpeak is the integrity parameter corresponding to the maximum shear stress point.

The fatigue life calculation formula is:

N_f = A(γ_max)^-B (7)

In the formula: A, B—fatigue-related coefficient,

A = f × (Df)^{[1 + (1 - C₂ )a] / {[1 + (1 - C₂ )a] × (πC₁ C₂ )a}} (8)

B=2a, f-loading frequency;
γ_max — expected maximum strain level (%)

To ensure the reliability and reproducibility of experimental results, all binder-scale and mixture-scale tests were conducted with at least 3 independent replicates (n = 3) per condition. The reported results represent the mean values of replicate measurements. The variability of experimental data was evaluated using standard deviation (SD), and error bars are provided in all relevant figures to reflect statistical dispersion. For LAS–S-VECD parameters, DSR rheological indices, and fatigue life from four-point bending tests, the coefficient of variation (COV) was additionally calculated to assess data consistency.

In all cases, statistical differences between modified and unmodified binders were examined to ensure that observed trends are not due to experimental scatter but represent statistically meaningful differences in fatigue and rheological behavior.

Four-point bending fatique testing
To validate binder-level fatigue indicators and establish cross-scale correlations, four-point bending fatigue tests were conducted on asphalt mixtures prepared using an AC-16C gradation^30,31. The aggregate gradation, apparent density, bulk specific gravity, and water absorption of each aggregate size, together with the properties of the mineral filler, are summarized in Table 2. The asphalt content of all mixtures was fixed at 4.8% to ensure consistency across different WMA formulations.

Sieve Size (mm)	Aggregate Category					Synthetic Grading (%)
	1# (10~20mm. 29%)	2# (5~10mm. 29.2%)	3# (3~5mm. 17%)	4# (0~3mm. 19%)	Mineral Powder (5.8%)
0.075	0	0.1	0	0.9	90.8	5.5
0.15	0.1	0.1	0	4.9	95.3	6.5
0.3	0.1	0.2	0	13	98.7	8.3
0.6	0.1	0.2	0	25.2	99.7	10.6
1.18	0.1	0.2	0	47.8	100	15
2.36	0.1	0.5	0	100	100	25
4.75	0.8	15.5	98.9	100	100	46.4
9.5	15.2	99.5	100	100	100	75.2
13.2	68.4	99.8	100	100	100	90.8
16	94.8	100	100	100	100	98.5
19	100	100	100	100	100	100
Apparent Relative Density	2.899	2.918	2.845	2.754	2.872	2.865
SSD Relative Density	2.854	2.847	2.816	2.691	－	2.814
Bulk Specific Gravity	2.829	2.81	2.8	2.655	－	2.787
Aggregate Water Absorption Rate (%)	0.85	1.32	0.56	1.36	－	－

Table 2: Grading of aggregates in warm-mix asphalt mixture. Table 2 presents the aggregate gradation of the warm-mix asphalt mixture, including the proportions of different aggregate fractions, mineral powder content, synthetic gradation curve, and aggregate physical properties. The table presents the designed particle-size distribution and the basic characteristics of the aggregates used in the asphalt mixture.

Four-point bending fatigue tests were performed using a Cooper testing apparatus under strain-controlled loading conditions to evaluate the fatigue durability of warm-mix asphalt (WMA) mixtures³². The failure criterion was defined as the number of loading cycles required for the flexural stiffness to decrease to 50% of its initial value. In accordance with the established testing protocol³³, cyclic loading was applied in the form of a continuous sinusoidal waveform at a frequency of 10 Hz under isothermal conditions of 15 °C. All tests were conducted without rest periods to ensure uninterrupted energy input during fatigue loading^34,35.

Beam specimens were fabricated in accordance with standard dimensional requirements, with a length of 381 ± 6.35 mm, a width of 63.5 ± 6.35 mm, and a height of 50.8 ± 6.35 mm³⁶³⁷. Under strain-controlled conditions, fatigue performance was characterized by plotting fatigue characteristic curves for specimens with different WMA formulations in a double-logarithmic coordinate system³⁸. A power-law constitutive relationship was subsequently established, and nonlinear regression analysis was employed to fit the fatigue data of the various asphalt mixtures, providing the basis for subsequent fatigue life modeling and comparative analysis^39,40,41. The beam specimen was mounted symmetrically in the four-point bending fixture, and contact between the loading clamps and specimen surface was checked before loading. The test was conducted at 15 °C under strain-controlled sinusoidal loading at 10 Hz without rest periods. The test endpoint was defined as the number of cycles at which flexural stiffness decreased to 50% of its initial value. Tests were considered valid when failure occurred within the gauge section, and no abnormal clamp slippage or sudden non-fatigue fracture was observed. All quantitative data are presented as mean ± standard deviation (mean ± SD), with sample size n = 3 for all experimental groups unless otherwise specified.

Results

Rheological properties of WMA
The asphalt–aggregate interfacial zone is widely recognized as the primary initiation site of fatigue cracking. Accordingly, the fatigue-related rheological parameter G*sin δ, measured at intermediate service temperatures, was employed to evaluate the fatigue performance of warm-mix asphalt (WMA) binders. Figure 1 presents the variation of G*sin δ for the original and warm-mix modified binders of Asphalt A, Asphalt B, and Asphalt C. All quantitative results are expressed as mean ± SD based on three repeated measurements (n = 3). Statistical comparisons between original and warm-mix modified binders at the same temperature were performed using an independent-samples t-test, and differences were considered significant at p < 0.05. As shown in Figure 1, G*sin δ decreases continuously with increasing temperature for all asphalt binders, indicating reduced fatigue-related stiffness at higher intermediate temperatures. For Asphalt A, AP exhibits significantly higher G*sin δ values than AO across the tested temperature range of 16–25 ˚ C (p = 0.025 (range: 0.018–0.032)), decreasing from 7685 ± 126 to 2480 ± 84 kPa, whereas AO decreases from 5580 ± 112 to 1535 ± 76 kPa. Similarly, BP shows significantly higher G*sin δ values than BO from 22 to 28 (p = 0.021 (range: 0.011–0.027)), with BP decreasing from 7980 ± 138 to 3985 ± 105 kPa and BO decreasing from 6120 ± 120 to 1725 ± 82 kPa. These results suggest that the warm-mix additive increases the fatigue factor of Asphalts A and B, leading to greater viscous energy dissipation and potentially higher fatigue susceptibility at the binder level. In contrast, Asphalt C shows only a slight difference between CO and CP; although CP is marginally higher than CO at the same temperature, the difference is not statistically significant at most temperatures (p = 0.086–0.214). Specifically, CP decreases from 13.420 ± 185 to 4420 ± 96 kPa, while CO decreases from 13.080 ± 172 to 4350 ± 91 kPa, indicating that the warm-mix additive has a limited influence on the fatigue-related rheological behavior of Asphalt C. Overall, the three binders exhibit different responses to warm-mix modification, reflecting the influence of asphalt source on fatigue performance. Asphalts A and B are more sensitive to the warm-mix additive, whereas Asphalt C maintains relatively stable fatigue resistance after modification.

In contrast, Asphalt C exhibits no significant change in G*sin δ after warm-mix modification, indicating that the warm-mix additive exerts a limited influence on its fatigue-related rheological properties. This observation suggests that the intrinsic chemical composition of Asphalt C dominates its viscoelastic response, thereby reducing the sensitivity of fatigue-related parameters to additive modification. These results highlight the oil–source–dependent nature of the warm-mix modification effect. Temperature sweep results reveal consistent rheological trends for all tested binders. As temperature increases, the rutting factor G*/sin δ decreases continuously, while the phase angle δ increases gradually, indicating a progressive transition toward viscous-dominated behavior. Elevated temperatures intensify molecular motion within the binder, weaken elastic structures, and reduce resistance to deformation. Conversely, increasing aging severity leads to higher G*/sin δ values and lower phase angles, reflecting enhanced stiffness and elastic response due to aging-induced hardening.

Figure 1. Fatigue factor (G*sin δ) of different asphalt binders as a function of temperature. (A) Asphalt A (Karamay); (B) Asphalt B (CNOOC 36-1); (C) Asphalt C (PetroChina/Venezuelan Boscan). AO, BO, and CO denote the original asphalt binders, whereas AP, BP, and CP denote the corresponding warm-mix asphalt binders. G*sin δ decreases with increasing temperature for all binders, while the influence of warm-mix modification varies depending on the binder source. Please click here to view a larger version of this figure.

These rheological evolutions can be attributed to the compositional changes of asphalt binders during thermal–oxidative aging. Low-molecular-weight components are gradually transformed into higher-molecular-weight structures through oxidation and polymerization reactions, increasing the complex modulus G*. At the same time, the accumulation of polar oxidation products enhances elastic energy storage, manifested as a reduction in phase angle. As aging progresses, the binder becomes increasingly sensitive to temperature variations, and the temperature dependence of fatigue-related rheological parameters becomes more pronounced.

Overall, the results demonstrate that the influence of warm-mix modification on binder fatigue-related rheological properties is strongly dependent on crude oil origin. While the warm-mix additive alters the viscoelastic dissipation behavior of certain binders, its effectiveness is constrained by the base asphalt's intrinsic composition and aging characteristics. These findings emphasize the need to consider oil–source–specific properties when interpreting DSR-based fatigue factors and assessing the fatigue performance of warm-mix asphalt binders. The aging-related increase in G·sin δ was quantified using the raw DSR data summarized in Figure 1. Percentage changes were calculated relative to the corresponding unaged binder condition.

Linear amplitude sweep
Key parameters derived from the S-VECD framework are summarized in Table 3. The integrity index C quantitatively characterizes the progressive degradation of asphalt binders under cyclic mechanical loading, with C = 1 representing the pristine, undamaged state and C = 0 corresponding to complete structural failure. In addition, the regression coefficients C₁ and C₂ describe the evolution of material integrity with increasing damage. Lower values of C₁ and C₂ indicate improved structural stability at equivalent damage levels, which is directly associated with enhanced fatigue resistance at the binder scale. As shown in Table 3, aging generally increases C₁ and decreases C₂, suggesting a deterioration in binder integrity evolution and fatigue resistance. Karamay asphalt shows the highest resistance to damage accumulation with the lowest C₁ and relatively high C₂ values, while CNPC asphalt exhibits the opposite trend, indicating weaker fatigue performance.

Asphalt Type	α	C₀	C₁	C₂	A	B
Karamay	1448855	1	0.0144	0.7346	2.93 × 10⁵	2.90 × 10⁶
Aged Karamay	1434103	1	0.0132	0.7412	3.00 × 10⁵	2.87 × 10⁶
CNOOC	1415228	1	0.0178	0.7112	2.25 × 10⁵	2.83 × 10⁶
Aged CNOOC	1400364	1	0.0155	0.7349	2.28 × 10⁵	2.80 × 10⁶
CNPC	1537043	1	0.0335	0.6077	4.38 × 10⁵	3.07 × 10⁶
Aged CNPC	1500600	1	0.0371	0.5822	4.41 × 10⁵	3.00 × 10⁶

Table 3: VECD method-related parameters. Table 3 summarizes the fitted model parameters for three asphalt binders under unaged and aged conditions. The parameter variations reflect the effects of asphalt type and aging on the model characteristics.

Figure 2 illustrates the damage evolution curves of different asphalt binders in both conventional and warm-mix modified conditions. Under identical stress levels, warm-mix asphalt (WMA) systems exhibit a noticeably lower damage accumulation rate than their conventional counterparts, indicating a more favorable damage evolution. This behavior suggests that warm-mix modification optimizes the mechanism of internal energy dissipation during cyclic loading, thereby improving fatigue resistance. The percentage changes in damage rate coefficients were calculated from the fitted S-VECD parameters listed in Table 3 using the unmodified binder as the reference condition.

Figure 2: Fatigue resistance characteristics across asphalt binder formulations. (A) Asphalt A; (B) Asphalt B; (C) Asphalt C. AO, BO, and CO represent the original asphalt samples, while AP, BP, and CP denote the corresponding warm-mix asphalt samples. Please click here to view a larger version of this figure.

A detailed examination of the damage evolution profiles reveals pronounced binder-dependent differences. Warm-mix modified Asphalt A demonstrates superior fatigue resistance relative to the unmodified binder, as evidenced by the more favorable positioning of its damage evolution curve. This result confirms that the warm-mix additive effectively enhances the durability of Asphalt A under repeated loading. In contrast, Asphalt B exhibits a negligible response to warm-mix modification, with both modified and unmodified binders following nearly identical damage progression trajectories. For Asphalt C, a threshold-dependent improvement is observed: the warm-mix modified binder outperforms the base asphalt only when the damage variable exceeds 100 units, indicating that the additive's effectiveness is primarily activated at advanced damage stages.

Quantitative comparisons of fatigue life derived from the LAS test are presented in Figure 3. The observed variations in fatigue performance further highlight the material-specific nature of the warm-mix additive–binder interaction, whose effectiveness is strongly governed by the intrinsic compositional characteristics of the base asphalt. Among the investigated materials, Qinhuangdao PetroChina asphalt exhibits the highest fatigue resistance, reflecting inherent advantages associated with its base feedstock composition. Conversely, Karamay asphalt shows the most pronounced improvement following warm-mix modification, underscoring the critical role of base asphalt properties in determining the performance enhancement potential of warm-mix additives.

Figure 3. Comparison of fatigue life between hot-mix asphalt (HMA) and warm-mix asphalt (WMA) for the three asphalt binders. The fatigue life differs only slightly between WMA and HMA for all three binder types. Asphalt C exhibits the highest fatigue life, followed by Asphalt A and Asphalt B. Overall, the results indicate that warm-mix modification produces only a modest effect on fatigue life, with the magnitude and direction of the change depending on the binder type. Please click here to view a larger version of this figure.

Although warm-mix modification generally improved fatigue performance, the magnitude of improvement was relatively modest for some binders. This behavior can be attributed to the mechanism of Evotherm M1, which mainly reduces production temperature and mitigates short-term oxidative aging rather than chemically reinforcing the binder structure. Therefore, fatigue enhancement is expected to be moderate and strongly dependent on the base asphalt's intrinsic characteristics. The consistency among replicate measurements indicates that the observed trends are reproducible despite the limited magnitude of improvement. To further interpret the observed binder-dependent fatigue behavior from a chemical perspective, the influence of crude oil composition on S-VECD parameters and fatigue performance was analyzed. The three binders exhibit distinct compositional characteristics: higher aromatic-to-saturate ratios are generally associated with improved stress redistribution and delayed damage accumulation, whereas higher asphaltene-rich systems tend to accelerate stiffness growth and reduce fatigue resistance.

In this study, Karamay-based asphalt exhibits a relatively higher aromatic fraction and lower saturate content, which corresponds to lower damage evolution rates (reduced C₁ values) and improved fatigue life in both LAS and mixture-scale tests. In contrast, the PetroChina-derived binder shows a more balanced, but relatively higher, saturated proportion, leading to intermediate S-VECD damage accumulation behavior. CNOOC-derived asphalt, with higher polarity-related fractions inferred from crude origin characteristics, demonstrates more rapid stiffness growth under cyclic loading, reflected in higher C₁ and reduced fatigue life. These results suggest that the aromatic-to-saturate balance governs viscoelastic energy dissipation pathways and microstructural damage evolution, thereby directly influencing S-VECD parameters and fatigue resistance. Overall, the current results should be viewed as a mechanistically grounded but boundary-conditioned framework, rather than a fully universal predictive model for all asphalt systems.

Mixture-scale fatigue resistance
The fatigue resistance of asphalt mixtures incorporating different warm-mix asphalt (WMA) technologies was systematically evaluated, and the corresponding fatigue test results are summarized in Table 4. These data quantify the endurance of asphalt mixtures under cyclic loading and reveal distinct differences in fatigue longevity among the investigated WMA formulations. The observed variability indicates that mixture-scale fatigue performance is strongly dependent on material composition and warm-mix technology.

Asphalt Type	Sample ID	Porosity (%)	Strain Level (με)	Fatigue Life (Cycles)
Karamay	1	4.5	100	22,36,902
	2	4.3	100	18,30,625
	3	3.7	100	19,49,138
	4	4.5	150	3,06,655
	5	5.3	150	3,97,762
	6	4.9	150	2,98,042
CNOOC	1	4.2	200	52,315
	2	5.1	200	58,828
	3	5.3	200	67,762
	4	3.8	75	6,47,145
	5	4.3	75	5,63,675
	6	4.5	75	6,91,698
CNPC	1	3.6	100	47,343
	2	4.1	100	24,149
	3	4.7	100	18,495
	4	3.5	200	4,412
	5	4.1	200	2,269
	6	4.7	200	3,299

Table 4: Fatigue test results of asphalt mixtures with different WMA. Table 4 summarizes the fatigue test results of asphalt mixtures with different warm-mixing technologies, including fatigue life and related performance parameters under various testing conditions. The results demonstrate the differences in fatigue resistance among the warm-mix asphalt mixtures and provide a basis for evaluating their fatigue performance.

The fatigue performance of bituminous composites is mathematically modeled through Equation (9), which quantifies cyclic stress degradation in pavement materials. This relationship formalizes the fatigue response of asphalt formulations under repeated loading conditions, serving as a computational framework for durability analysis:

(9)

In the formula: N_f——Fatigue Life of Asphalt Mixture;
ε——strain;
k, n——coefficient.

Based on Equation (9), regression analysis was performed for each asphalt mixture to calibrate the corresponding fatigue model parameters. The resulting coefficients k and n provide a quantitative representation of mixture-specific fatigue-degradation characteristics and enable direct comparison of fatigue performance across different WMA formulations. The calibrated fatigue equation parameters are summarized in Table 5.

Types of Asphalt	Fatigue Equation	k	n	R2
A	y = 2.463 × 1016x−5.029​	2.463 × 1016	5.029	0.993
B	y = 1.713 × 1015x−5.120​	1.713 × 1015	5.12	0.965
C	y = 1.233 × 1019x−5.975​	1.233 × 1019	5.975	0.964

Table 5: Fatigue equation parameters of asphalt mixtures with different WMA. Table 5 summarizes the fatigue equation parameters of asphalt mixtures with different warm-mixing technologies, including the regression coefficients and model parameters used to describe the relationship between fatigue life and loading conditions. These parameters provide a quantitative basis for predicting fatigue performance and comparing the fatigue resistance of different warm-mix asphalt mixtures.

Figure 4 presents fatigue life–strain relationships for asphalt mixtures with different WMA types, based on the fitted fatigue models. As expected, the fatigue life of all mixtures decreases systematically with increasing strain amplitude, consistent with classical fatigue behavior of bituminous composites. Comparative analysis of the fatigue curves reveals a clear hierarchy in mixture fatigue resistance, with the overall performance ranking determined as Material C > Material A > Material B. This ranking reflects the relative ability of each mixture to sustain repeated loading cycles before failure and is consistent with the regression parameters summarized in Table 5.

Figure 4: Fatigue patterns of asphalt mixtures with different warm-mixing types. As shown in Figure 4, the fatigue life of all asphalt mixtures decreased with increasing strain level. Among the three warm-mixed asphalt mixtures, mixture C exhibited the highest fatigue resistance, followed by mixtures A and B. The significantly higher fatigue life of mixture C indicates that this warm-mixing technology effectively improves the resistance of asphalt mixtures to fatigue damage accumulation. Please click here to view a larger version of this figure.

Under equivalent air void conditions, WMA technology provides notable fatigue performance benefits by reducing production and compaction temperatures by approximately 20–30 °C. This temperature reduction mitigates short-term oxidative aging of asphalt binders, which is a primary driver of long-term embrittlement. By preserving binder viscoelasticity and stress dissipation capacity, WMA suppresses microcrack initiation and propagation under cyclic loading. Consequently, cumulative fatigue damage is alleviated, resulting in enhanced mixture fatigue life and improved pavement durability. These advantages are critical for extending service life, reducing maintenance demands, and enabling the development of more durable and cost-effective pavement infrastructure. To examine the consistency between binder-scale and mixture-scale fatigue behavior, correlations between the binder fatigue factor G*sin δ and mixture fatigue life N_f were analyzed, as shown in Figure 5. A statistically significant relationship is observed for all binders, indicating that binder rheological properties exert a measurable influence on mixture fatigue performance. Notably, Binder B exhibits an exceptionally strong correlation (R² = 0.99, p < 0.001), suggesting that G*sin δ serves as a reliable predictor of mixture fatigue life for this material. In contrast, Binders A and C show comparatively weaker correlations (R² = 0.6051 and 0.7933), implying that binder rheology alone cannot fully capture mixture fatigue behavior for these systems.

Figure 5: Correlation between asphalt fatigue factor G*sin δ and mixture fatigue life N_f. (A) Asphalt A; (B) Asphalt B; (C) Asphalt C. Figure 5 indicates that G∗sinδ shows a positive correlation with mixture fatigue life, with Asphalt B exhibiting the highest consistency, followed by Asphalt C and A. Please click here to view a larger version of this figure.

Further cross-scale validation was conducted by correlating binder damage evolution parameters obtained from LAS tests, interpreted using the Simplified Viscoelastic Continuum Damage (S-VECD) framework, with mixture fatigue life. As illustrated in Figure 6, strong linear correlations are observed between progressive binder degradation and mixture fatigue performance. For all three binders, the correlation coefficients exceed 0.9, demonstrating a robust and consistent linkage between binder-level damage characteristics and mixture-scale fatigue resistance.

Figure 6: Correlation between asphalt fatigue damage and mixture fatigue life N_f. (A) Asphalt A; (B) Asphalt B; (C) Asphalt C. As shown in Figure 6, asphalt fatigue damage exhibited a strong positive correlation with the fatigue life Nf of asphalt mixtures. High determination coefficients were obtained for Asphalt A, B, and C, indicating that fatigue damage parameters can effectively characterize the fatigue performance of asphalt mixtures. Compared with the conventional binder fatigue factor G∗sinδ, fatigue damage provides a more direct representation of the fatigue deterioration behavior of asphalt mixtures. Please click here to view a larger version of this figure.

Overall, the mixture-scale fatigue results confirm that fatigue performance is jointly governed by mixture composition, warm-mix technology, and binder characteristics. While conventional rheological indicators provide limited predictive capability for certain binders, LAS–S-VECD-based damage metrics demonstrate strong and consistent correlations with mixture fatigue life. These findings validate binder-scale damage characterization as an effective surrogate for evaluating mixture durability and provide a mechanistic foundation for performance-based pavement design. The distinctly different responses of the three asphalt binders to warm-mix modification can be fundamentally attributed to variations in their crude oil–derived chemical composition and resulting colloidal structures. Asphalt binders are typically considered colloidal systems composed of asphaltenes dispersed in a maltene phase comprising aromatics, resins, and saturates. The balance among these fractions governs the binder's sensitivity to external modifiers, such as warm-mix additives. For Karamay asphalt (Binder A), the relatively high resin content and low paraffin fraction lead to a more dispersed asphaltene network with weaker internal structural stability. In this system, the introduction of the warm-mix additive significantly alters the viscosity and molecular mobility, resulting in enhanced energy dissipation and increased G*sin δ values. This indicates that the additive actively modifies the internal phase interaction, making the binder more susceptible to cyclic deformation and thus accelerating fatigue damage accumulation at the binder scale.

In contrast, CNOOC-derived asphalt (Binder B) exhibits a more balanced naphthenic-based composition with a stable colloidal structure. The asphaltene–resin equilibrium in this binder provides a relatively robust internal network, which limits the penetration and structural influence of the warm-mix additive. As a result, minimal changes in rheological and damage evolution behavior are observed, indicating that the additive effect is largely constrained by the intrinsic stability of the binder microstructure. For PetroChina-derived asphalt (Binder C), the higher polarity-related fractions and increased asphaltene complexity result in a more rigid and aggregation-prone microstructure. In this case, the warm-mix additive appears to exhibit a threshold-dependent activation behavior, where its influence becomes more pronounced only after significant damage accumulation. This suggests that the additive does not strongly interact with the initial colloidal structure but instead affects the later-stage damage evolution process by modifying stress redistribution pathways.

Overall, these results demonstrate that the effectiveness of warm-mix modification is not universal but strongly governed by the intrinsic colloidal stability and chemical composition of the base asphalt. The observed differences in S-VECD damage evolution and mixture fatigue performance can therefore be directly linked to the microstructural heterogeneity of the three binders, providing a mechanistic explanation for the oil-source-dependent behavior observed in both rheological and fatigue tests.

DATA AVAILABILITY:
All data, models, and code generated or used during the study are available in the supplementary folder named “Raw data”.

Discussion

This study proposes a cross-scale fatigue evaluation framework that integrates binder-level Linear Amplitude Sweep (LAS) testing with the Simplified Viscoelastic Continuum Damage (S-VECD) model and mixture-level four-point bending fatigue testing to establish a mechanistic linkage between asphalt binder damage evolution and mixture fatigue performance. Unlike conventional fatigue evaluation approaches that primarily rely on empirical rheological indicators, such as G*·sin δ, the proposed framework utilizes damage-related parameters derived from continuum damage mechanics to characterize the intrinsic degradation behavior of asphalt binders under cyclic loading. By incorporating crude-oil origin of asphalt as an influencing factor, this study further demonstrates that the effectiveness of warm-mix modification is not universal but strongly depends on the chemical composition and colloidal structure of the base binder. These findings provide new insights into the interaction among crude source, warm-mix additives, aging susceptibility, and fatigue resistance, thereby establishing a more mechanistically based approach for asphalt material evaluation. Previous studies have highlighted the potential of LAS–S-VECD analysis for binder fatigue characterization; however, its direct applicability for predicting mixture-scale fatigue performance remains under continuous investigation. The present work contributes to this research area by validating the cross-scale relationship between binder damage evolution and mixture fatigue behavior across multiple binder systems.

The proposed framework advances the scientific understanding of asphalt fatigue mechanisms by bridging the gap between binder-scale rheological characterization and mixture-scale structural performance. Traditional binder evaluation methods often provide limited information on the progressive accumulation of fatigue damage, as parameters such as the complex modulus and phase angle primarily describe instantaneous viscoelastic responses rather than damage evolution. In contrast, the S-VECD approach considers asphalt binders as continuously degrading viscoelastic materials and provides quantitative descriptors of structural integrity loss during fatigue loading. The strong correlations obtained between LAS–S-VECD parameters and mixture fatigue life in this study indicate that binder-level damage evolution can provide meaningful information regarding the initiation stage of mixture cracking. Similar findings have suggested that mechanistic damage-based parameters may offer improved predictive capability compared with conventional rheological indices. Therefore, this study extends current asphalt fatigue research by providing experimental evidence that binder-scale damage mechanics can serve as a bridge toward performance-based pavement material design.

Despite the promising results, several limitations should be acknowledged. First, the current investigation was conducted using three asphalt binders derived from specific crude oil sources and one aggregate gradation; therefore, the universality of the proposed relationship requires further validation using a broader range of binders, modification technologies, and mixture designs. Although the selected binders represent typical pavement materials used in engineering practice, asphalt materials exhibit considerable variability due to differences in crude origin, refining process, and chemical composition. Second, laboratory fatigue tests were performed under controlled temperature and loading conditions, whereas actual pavement structures experience complex environmental factors, including temperature fluctuations, moisture infiltration, traffic load variability, and long-term aging. Third, although LAS–S-VECD parameters showed strong correlations with mixture fatigue performance, the current dataset is insufficient to establish a universal predictive model applicable to all asphalt systems. Therefore, future studies should incorporate larger databases and field performance observations to further improve the robustness and transferability of the proposed approach.

Alternative approaches may also be considered to further investigate the relationship between binder damage evolution and mixture fatigue performance. For example, advanced chemical characterization techniques, including Fourier-transform infrared spectroscopy (FTIR), nuclear magnetic resonance (NMR), and molecular dynamics simulation, could provide additional insights into the molecular mechanisms governing oil-source-dependent fatigue behavior. Previous studies have demonstrated that variations in asphalt molecular structure, including asphaltene aggregation, aromatic distribution, and polarity-related interactions, significantly influence rheological response and aging susceptibility. In addition, advanced imaging techniques, such as atomic force microscopy (AFM) and X-ray-based characterization methods, could be employed to directly observe microstructural evolution during fatigue damage accumulation. Combining these approaches with LAS–S-VECD analysis may provide a more comprehensive understanding of the relationship between molecular structure, binder damage mechanics, and macroscopic pavement performance.

The proposed LAS–S-VECD-based methodology has important potential applications in several areas of asphalt pavement engineering and material science. From a practical perspective, this framework can be used as an efficient screening tool for evaluating candidate binders, selecting appropriate warm-mix additives, and assessing aging sensitivity before conducting time-consuming mixture-scale fatigue experiments. Compared with traditional empirical specifications, the proposed approach provides a mechanistic basis for performance-oriented pavement design by directly linking binder damage characteristics with structural durability. This is particularly valuable for sustainable pavement technologies, where the increasing application of warm-mix asphalt, recycled materials, and alternative binders requires reliable methods for predicting long-term performance. Furthermore, the methodology may contribute to the development of data-driven pavement design systems by providing physically meaningful fatigue descriptors that can be integrated with predictive models and life-cycle assessment frameworks.

Future research should focus on expanding the applicability of the proposed framework toward more comprehensive and field-oriented pavement performance prediction. Future studies should include larger binder databases covering different crude sources, polymer-modified binders, recycled asphalt materials, and emerging sustainable modifiers to establish more generalized fatigue prediction models. Moreover, the integration of LAS–S-VECD analysis with multi-scale characterization methods, artificial intelligence approaches, and molecular-level simulations may further improve the understanding and prediction accuracy of asphalt fatigue behavior. Long-term field monitoring and accelerated pavement testing should also be incorporated to validate laboratory-based predictions under realistic service conditions. Ultimately, the combination of mechanistic damage modeling, advanced material characterization, and performance-based design strategies is expected to facilitate the development of more durable, sustainable, and reliable asphalt pavement systems.

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Binder A / AO, Karamay asphalt	Karamay crude oil source, China	N/A	Base asphalt binder
Binder B / BO, CNOOC 36-1 asphalt	CNOOC 36-1 offshore crude oil source, China	N/A	Base asphalt binder
Binder C / CO, PetroChina asphalt	PetroChina / Venezuelan Boscan crude-based source	N/A	Base asphalt binder
Evotherm M1 warm-mix additive	Ingevity / MeadWestvaco	Evotherm M1	Warm-mix additive for WMA binder preparation
Dynamic Shear Rheometer	Malvern	Kinexus DSR+	Used for DSR temperature sweep and LAS tests
Rolling Thin Film Oven Test device	Shanghai Changji	SYD-0610	Used for short-term aging
Pressure Aging Vessel	InstroTek	PAV-9300	Used for long-term aging
Four-point bending fatigue testing system	Cooper Research Technology	SA4PT	Used for strain-controlled mixture fatigue tests
S-VECD analysis framework	data analysis	N/A	Used to calculate LAS-derived damage parameters
Data analysis software	Origin	OriginPro 2024	Used for regression fitting, correlation analysis, and plotting