Mesoscopic Fatigue Damage and Critical Frequency Response of Saturated AC-20 Asphalt Concrete Based on Discrete Element Simulation

Abstract

Water damage under the coupled effects of traffic load and pore water pressure (PWP) is a primary cause of early failure in asphalt pavements. Although dense-graded pavements generally have low void ratios, excess PWP poses a severe threat to durability under extreme conditions. These conditions include heavy rainfall, water accumulation in wheel tracks, and upward capillary water rise. In this study, a mesoscopic model considering fluid–solid coupling effects was established using the Particle Flow Code in the 2 Dimensions (PFC2D) platform, which is based on the discrete element method (DEM). A parallel-bonded stress corrosion model was introduced to describe damage evolution. The results show that the maximum positive PWP increased monotonically with load, reaching a distinct peak value at a critical loading frequency under specific load amplitudes. At this critical frequency, the fatigue life was significantly shortened compared to lower-frequency conditions. The PWP response exhibited a clear phase lag relative to the applied load, with the lag angle increasing alongside frequency. Furthermore, the absolute value of the minimum PWP continued to increase with fatigue damage accumulation. This indicates that regions with a vacuum suction effect were continuously expanding, which is a key reason for asphalt film stripping from the aggregate surface. These findings provide a theoretical basis for understanding mesoscopic water damage mechanisms in asphalt pavements and offer a reference for durability design.

1. Introduction

Dynamic pore water pressure (PWP) generated in saturated asphalt concrete under traffic load has been widely recognized as one of the main causes of water damage [1]. Field monitoring and laboratory test results show that vehicle movement can produce alternating positive and negative cyclic PWP inside the pavement structure, and this “pumping effect” may induce cracking at the asphalt–aggregate interface [2]. The amplitude of PWP generally increases with the increase in applied load, and this trend has been verified in steady-state vibration tests and field measurements based on fiber Bragg grating [3,4]. In addition, loading frequency also has a significant impact on the fatigue performance of asphalt mixtures [5]; higher loading frequencies will intensify the dynamic water-scouring effect and further increase the PWP level, thereby accelerating crack propagation and leading to a significant decrease in fatigue life within a specific frequency range [6,7,8].

It should be noted that although the void ratio of dense-graded asphalt mixtures is usually controlled between 3% and 5%, making full saturation difficult under normal service conditions, near-saturation or even full saturation may still occur in several engineering scenarios [9,10]. For example, water can continuously infiltrate the pavement structure layer during prolonged heavy rainfall with poor pavement drainage; water accumulates locally in the wheel tracks, and water is forced into the connected pores under the combined action of water film pressure and tire rolling; additionally, bottom-up water accumulation is caused by upward capillary water rise from the base course and water vapor condensation at the bottom of the surface layer. Furthermore, existing studies have shown that when the void ratio of compacted asphalt mixtures is in the range of 5% to 15%, it is relatively easy to form non-dissipative excess PWP under vehicle load, and this interval is regarded as a high-incidence range for water damage. Therefore, this study takes the fully saturated state as the most unfavorable working condition, aiming to explore the occurrence mechanism of water damage under extreme conditions and provide a reference for pavement drainage design and material water-stability evaluation.

In terms of hysteresis characteristics, existing studies have confirmed that there are phase lag and dissipation phenomena in PWP response relative to the applied load, and denser mixtures tend to exhibit stronger hysteresis effects and longer dissipation times [11,12]. Although numerical studies based on physical–mechanical coupling models and the finite-element method have enhanced the understanding of the water damage process in asphalt pavement structures, most existing models treat asphalt concrete as a homogeneous continuum or focus only on a single physical process, making it difficult to simultaneously reproduce the random distribution characteristics of PWP, the progressive damage evolution of interparticle bonds, and the fully coupled process of macroscopic failure at the mesoscopic scale. In contrast, the DEM has unique advantages in simulating complex multi-field interactions in granular materials.

Overall, although the above studies have advanced the understanding of asphalt pavement water damage from different perspectives, there are still the following deficiencies [13,14]. First, finite-element models based on continuum mechanics usually treat asphalt concrete as a homogeneous body, which makes it difficult to capture the mesostructural characteristics of aggregate–mastic–voids. Thus, they cannot effectively reproduce the spatial non-uniform distribution of PWP and the progressive fracture process of particle contacts. Second, although existing laboratory tests have confirmed the phase lag between load and PWP, there is still a lack of in-depth quantitative analysis on the mesoscopic mechanism of this phenomenon, that is, how the alternating positive and negative seepage processes in the pore network under alternating loads induce the lag of pressure response at the system level. Third, the systematic influence of loading frequency on the accumulation law of excess PWP and fatigue life has not been fully reported, and studies on the possible critical frequency (or “resonance” frequency) are still relatively limited.

Given that the existing homogenized finite-element models find it difficult to capture the mesoscopic characteristics of particle contact fracture and local PWP concentration [15,16], this study adopts the DEM to establish a fluid–solid coupling model through the Particle Flow Code within the 2 Dimensions (PFC2D, version 5.00) platform, and explores the excess PWP response and fatigue life of saturated AC (Asphalt Concrete)-20 asphalt mixtures under different loads (600–800 kPa) and frequencies (10–100 Hz). Although the two-dimensional model has certain limitations in the quantitative characterization of pore connectivity, this study focuses on quantitatively highlighting the mesoscopic mechanism of load–PWP hysteresis as a cross-scale seepage phenomenon using DEM, which was not captured by previous continuum-based models. Additionally, the study determines and evaluates a certain critical frequency that exacerbates water damage. The practical significance of this work is that it provides a theoretical basis for durability design and suggests that pavement evaluation should consider the resonance between vehicle speed and the pavement’s internal drainage characteristics.

2. Methods

2.1. Discrete Element Method and Fluid–Solid Coupling Theory

The discrete element method (DEM) was proposed by Cundall [17], initially for rock mechanics analysis, and later extended to soil mechanics by Cundall and Strack [18]. This method regards granular materials as an assembly of discrete particles, and simulates their motion by solving Newton’s second law of motion for each particle individually without presetting macroscopic constitutive relations. The interaction between particles is calculated through contact detection and contact constitutive models [19,20], and the particle velocity and displacement are updated iteratively using explicit time integration [21,22]. The calculation cycle in PFC2D is shown in Figure 1.

Compared with the finite-element method, the DEM has the following characteristics when simulating water damage of asphalt mixtures [23]: it can explicitly characterize the three-phase mesostructure of aggregate–mastic–voids; the fracture and slip of interparticle bonds can occur naturally without presetting crack paths; the seepage and pressure accumulation of water can be directly simulated at the pore scale through the domain-pipe coupled fluid network. These characteristics enable the DEM to reproduce the spatial non-uniform distribution of PWP and the progressive damage induced by it at the mesoscopic scale.

In PFC2D, the pipe is modeled as a virtual channel connecting adjacent domains, which is used to calculate fluid flow driven by pressure difference, as shown in Figure 2. The fluid flow rate in the pipe network is formulated based on the intrinsic permeability and fluid dynamic viscosity, which ensures the theoretical consistency of the fluid–solid coupling framework.

2.2. AC-20 Discrete Element Model

2.2.1. PFC2D Model of AC-20

Based on the gradation of AC-20 shown in

Table 1. Gradation of the PFC2D model for AC-20.

Size (mm)	0.075	0.15	0.3	0.6	1.18	2.36	4.75	9.5	13.2	16	19	26.5
Percent passing (%)	5	8.9	13.1	16.2	23.4	31.3	39.5	52.9	67.2	79.9	94.8	100

, a two-dimensional discrete particle model (100 mm in diameter and 150 mm in height) was established, as shown in Figure 3. The model contains 135 particles with particle sizes ranging from 2.36 mm to 26.5 mm, and the initial void ratio is set to 8.7%, which is in the middle of the high-incidence range of water damage (5%~15%) and close to the critical value of water damage occurring in the field [24]. The corresponding initial permeability coefficient 1.118 × 10⁻⁴ m/s is determined by the void ratio–permeability coefficient exponential relationship, as shown in Figure 4. The remaining mechanical parameters of the model are shown in

Table 2. Parameters of the PFC2D model for AC-20.

Linear Contact Modulus (Pa)	Parallel Bond Modulus (Pa)	Kn/ks	pb_ten (Pa)	pb_coh (Pa)	pb_fa (°)
4.3 × 107	3.2 × 108	2.8	4.04 × 106	2.04 × 106	35

, and were calibrated, as by Zhang [25], by matching the PFC2D uniaxial compression simulation results with laboratory test results. The deviations of elastic modulus and peak strength are controlled within 5%.

The volume fractions are respectively 0.1917 for the range of 4.75mm to 9.5mm, 0.2082 for the range of 9.5mm to 13.2mm, 0.3041 for the range of 13.2mm to 16mm, 0.2169 for the range of 16mm to 19mm, and 0.0757 for the range of 19mm to 25mm.

The two-dimensional approximation adopted in this study has limitations: there are differences in pore connectivity and flow cross-section compared with the three-dimensional reality, which may affect the estimation of permeability coefficient and PWP dissipation rate. The number of particles is limited to 135 mainly due to the time step requirement of the fluid–solid coupling calculation.

In Table 1, the volume fraction refers to the proportion of the total volume of the model occupied by particles between two adjacent particle sizes. For example, the volume fraction of particles with sizes from 2.36 mm to 4.75 mm is 0.1917.

It is important to note that this two-dimensional (2D) approximation has inherent limitations in representing pore connectivity and flow cross-sections, compared to 3D realities. Therefore, this model is designed and validated solely for qualitative mechanistic analysis and to reveal physical trends (e.g., the non-monotonic frequency response and the hysteresis effect). The quantitative results, such as absolute PWP values, are not intended for direct engineering calculations without further 3D calibration.

2.2.2. Parallel-Bonded Stress Corrosion Model

The contact between particles in the model adopts a combination of linear contact and parallel bond [23]. The fatigue damage at the asphalt–aggregate interface is simulated by reducing the parallel bond diameter, following the parallel-bonded stress corrosion model proposed by Potyondy [26], as shown in Figure 5. Its attenuation law is controlled by Equation (1):

$${\displaystyle \frac{d\overline{D}}{dt}}={\beta }_1{\left({\displaystyle \frac{\sigma }{{\sigma }_c}}\right)}^{{\alpha }_1}{t}^{{\beta }_2{\left({\displaystyle \frac{\sigma }{{\sigma }_c}}\right)}^{{\alpha }_2}}$$

(1)

where $\overline{D}$ is the parallel bond diameter (m), σ is the interface normal contact force (Pa), and σ_c is the interface bond strength (Pa). The damage parameters were calibrated by indirect tensile creep tests on AC-20 asphalt mortar under three stress ratios (0.3, 0.4, and 0.5). First, the stiffness modulus attenuation curve, as shown in Figure 6a, was drawn, and the values of m and k were obtained by fitting with the power in Equation (2).

$$E\left(t\right)=m{t}^k$$

(2)

This was then converted into the attenuation rate of parallel bond diameter. After fitting with the stress ratio, each parameter was determined, as ${\mathsf{\beta }}_1=7.01\times {10}^{-6}$, ${\mathsf{\alpha }}_1=-0.9197$, ${\mathsf{\beta }}_2=-1.523$, ${\mathsf{\alpha }}_2=0.070$, and ${\mathsf{\sigma }}_{\mathrm{c}}=1\times {10}^5$. The validity of the model has been verified by two-particle tensile damage simulation, and the obtained damage simulation curve is shown in Figure 6b. The similar characteristics of the two curves indicate that the model and parameters are appropriate [24].

2.2.3. Loading Conditions and Boundary Settings

A dynamic load was applied to the top of the model to simulate the tire rolling process, and the schematic diagram of the rolling process is shown in Figure 7. The half-sine function expression of the dynamic load is as follows:

$$F\left(x,t\right)=A{sin}^6\left(\omega t\right)$$

(3)

In Equation (3), where A is the load amplitude (600, 700, 800 kPa), $\omega =2\pi f$ (The f is 10, 50, 100 Hz), and the power exponent 6 reflects the transient distribution characteristics of tire contact pressure. During the simulation, the dynamic viscosity of water was set to 1 × 10⁻³ Pa⋅s (normal temperature water at 25 °C), and the boundary flow velocities at the bottom edge and left and right sides of the model were set to zero to simulate the blocking effect of the underlying structure on water flow. In this study, the fatigue life is defined as the loading time until the first particle is detached from the asphalt mixture model, indicating the onset of structural failure due to complete bond breakage around an aggregate.

This closed boundary condition represents a conservative, worst-case scenario in which drainage is completely obstructed (e.g., by an impermeable underlying layer or full water saturation). It is intended to maximize the excess PWP response, in order to study the damage mechanism. In reality, pavements have varying drainage capacities; thus, the presented peak PWP values represent an upper bound, and the fatigue lives are likely a lower bound.

2.3. Implementation of Fluid Coupling in PFC2D

2.3.1. Fluid Formulation for PFC2D

In the two-dimensional AC-20 model, pore domains and pipelines were delineated for the calculation of PWP, as depicted in Figure 8. The blue circles signify the pore domains, which were interconnected via blue lines denoting the pore pipelines. Each pipeline linking two adjacent domains represented a potential crack trajectory, corresponding to a bond contact point prone to failure (refer to Figure 8). Under a pressure gradient, fluid flowed from neighboring domains into a specific domain, giving rise to infiltration pressure. Concurrently, external loading instigated the deformation of the domains, generating excess PWP.

Each pore domain received flow from adjacent pore domains. With inflow defined as positive, the increment in fluid pressure over a time step Δt was calculated using Equation (4).

$$\mathsf{\Delta }P={\displaystyle \frac{E_f}{V_d}}\left(\sum q\mathsf{\Delta }t-\mathsf{\Delta }{V}_d\right)$$

(4)

In Equation (4), $E_f$ represents the bulk modulus of the fluid. For instance, at room temperature, the bulk modulus of water was typically taken as 2.20 × 10⁹ Pa. $V_d$ denoted the apparent volume of the pore domain. The first term on the right-hand-side of Equation (4) represented the increase in water volume within the domain, corresponding to the infiltration pressure. The second term represented the pressure change induced by the volumetric change of the pore domain, referred to as the hydrostatic pressure. The calculation of hydrostatic pressure necessitated the determination of both the apparent volume of the domain and its variation.

The thick red line in Figure 9 represented a hypothetical pipe connecting white domains A and B, and which was perpendicular to the contact force chain (green line) between particles 2 and 1. In PFC2D, the pipe was modeled as a parallel plate channel with a specific length (L), aperture (D), and unit depth (in the out-of-plane dimension). When the pressure in domain A exceeded that in domain B, water flowed from domain A to domain B, and the flow rate was calculated using Equation (5).

$$q={\displaystyle \frac{k}{\mu }}\times {\displaystyle \frac{(P_A-P_B)}{L}}\times D$$

(5)

In Equation (5), k is the intrinsic permeability (m²), μ is the dynamic viscosity (Pa⋅s), and $P_A-P_B$ is the pressure difference between two adjacent domains. A positive pressure difference indicates that fluid flows from domain A to domain B. The channel length L (m) was defined as the sum of the radii of the particles in contact with the adjacent domains. In porous media, the crack aperture D is a function of the normal stress and was described by the empirical Equation (6). This formula ensured a residual aperture when the normal load was zero, a value which gradually decreased as the load increased. Note that compressive forces were defined as positive; therefore, Equation (6) was applicable only to compressive normal forces.

$$D={\displaystyle \frac{D_0{F}_0}{F+F_0}}$$

(6)

In Equation (6), $F_0$ is the normal force, which was the value when the crack aperture was reduced to $D_0/2$. It should be noted that if the contact force was greater than the expected value, the crack aperture would remain unchanged at its residual value.

When the normal force was tensile (no adhesion) or zero, the crack aperture was equal to the sum of the residual aperture and the normal distance between the two particle surfaces.

$$D=D_0+mg$$

(7)

In Equation (7), the normal distance needs to be multiplied by a dimensionless m value; this does not represent a unit correction. In Equations (5)–(7), residual aperture $D_0$ was calculated according to Equation (8) [27,28].

$$D_0=\sqrt[3]{{\displaystyle \frac{12k\pi \sum _{balls}{R}^2}{\sum _{pipes}L}}}$$

(8)

In Equation (8), k is the intrinsic permeability, R is particle radius, and L is the length of the pipe.

As mentioned earlier, a domain is not a void but a specific closed spatial volume composed of a set of particles. Therefore, in a topological sense, a “domain” is a closed loop, as shown in Figure 5, in which the diagonal region is the domain formed by particles.

Furthermore, the center coordinates and apparent volume of a domain were approximated by calculating the coordinates and shape of the particles surrounding the domain, as detailed in Equation (9) [29,30].

$$\{\begin{array}{c}{x}_d={\displaystyle \frac{1}{N}}{\displaystyle \sum _1^N}{x}_i\\ y_d={\displaystyle \frac{1}{N}}{\displaystyle \sum _1^N}{y}_i\\ V_d=({\displaystyle \frac{1}{N}}{\displaystyle \sum _1^N}{R}_i)·{\displaystyle \frac{1}{N}}{\displaystyle \sum _1^N}\left[{\left(x_i-x_d\right)}^2+{\left(y_i-y_d\right)}^2\right]\end{array}$$

(9)

To account for the influence of particle shape on the apparent volume of the domain, it was necessary to multiply by the porosity. Here, porosity was the average porosity of the entire model.

2.3.2. Mechanical Coupling

To simplify the process of calculating the pressure exerted on particles, it was assumed that the pressure gradient along the pipeline is limited to the corresponding contact points. Subsequently, the pressure distribution within the domain was uniform, and the drag force $F_i$ was independent of the fluid flow path around the domain. If a polygonal path was selected that connects the contact points related to the domain, the force vector acting on a typical particle was calculated using Equation (10).

$$F_i=P{n}_{i}S$$

(10)

In Equation (10), $n_i$ represents the unit normal vector of the line connecting the two contact points, S represents the length of the line, and P is PWP, as shown in Figure 10.

The relationship between permeability coefficient and stress is described by Equation (11), as determined by the previous research of the research group [24].

$$k=1.118\times {10}^{-4}{e}^{-0.001\times \sigma }$$

(11)

3. Results and Discussion

3.1. Effect of Load on PWP

In general, higher loads lead to more significant deformation of the pore structure, thereby causing an increase in excess PWP. This monotonic trend is consistent with the triaxial test results reported in the previous research [31], where higher deviatoric stress generated higher excess PWP. The relationship curves between the maximum excess PWP and loading time in the AC-20 model are shown in Figure 11.

As shown in Figure 11, the maximum excess PWP under 700 kPa and 50 Hz reaches approximately 4.6 MPa; the excess PWP in the AC-20 model increased significantly with the increase in load. When the load gradually decreased to the contact load level (see Equation (5)), the PWP dropped sharply from the peak to the trough. As time went on, the PWP first rose briefly to form a small peak, then dropped again to the trough. Subsequently, the PWP rose briefly to form a new peak, but finally returned to the trough and stabilized as a horizontal line. The reason for this phenomenon is that during the unloading process, the aggregate particles around the domains with high PWP rebound rapidly expanded [32], causing the aggregate particles around other adjacent domains to undergo slight compression, thus generating a small PWP. Due to the small displacement compression, the generated PWP is also relatively low. As the unloading time increases, the aggregate particles around the domains stop moving, and the PWP in all domains tends to be consistent at this time.

Both maximum and minimum PWPs can be observed in the model. The relationship curves between the minimum PWP and loading time are shown in Figure 12.

Figure 12 shows the curves of the minimum PWP in the model with time, under different loads. As can be seen from Figure 12, the absolute value of PWP also increased with the increase in load; when the load was unloaded from the maximum value to the contact load, the curve presented several small peaks. This indicates that in the model, when a large negative PWP value disappears, a smaller negative PWP value will form at other positions until all negative PWP values in the model tend to be consistent. This is because a larger load causes greater pore deformation, thereby generating a larger PWP.

As the fatigue process progressed, the maximum value of PWP remained stable, while the absolute value of the minimum value increased, and the average value tended to be negative, as shown in Figure 13, Figure 14 and Figure 15. This indicates that the number of domains with volume expansion (negative pressure) in the model is increasing, reflecting the accumulation of damage, which leads to more regions experiencing rebound or microcrack opening during the unloading process and intensifies the vacuum suction effect. This is particularly unfavorable for the stripping of asphalt film.

3.2. Effect of Loading Frequency on PWP

Under the same load condition of 700 kPa, the PWP was significantly affected by the loading frequency, as shown in Figure 16.

It can be seen from Figure 16 that the maximum PWP value at 50 Hz was greater than those at 10 Hz and 100 Hz. However, the maximum PWPs at 10 Hz and 100 Hz were almost equal. This result indicates that under the simulation conditions of this study, the effect of loading frequency on the maximum positive PWP presents a non-monotonic characteristic, a peak appears at 50 Hz, while the pressure responses are weaker at both lower (10 Hz) and higher (100 Hz) frequencies. This suggests that there is a specific loading frequency at which the PWP response is the most significant. It also indicates that the effect of vehicle speed on the maximum positive PWP of asphalt pavement is not a simple monotonic increase or decrease, but there is a specific vehicle speed (equivalent to 50 Hz) at which the PWP generated inside the asphalt pavement is the most significant. The selected frequency range of 10–100 Hz closely represents the dynamic traffic spectrum encountered in real-world engineering. Specifically, a lower frequency of 10 Hz corresponds to heavy vehicle loads at low speeds or creeping traffic conditions (e.g., near urban intersections), while intermediate to higher frequencies of 50–100 Hz successfully match vehicles traveling at typical cruising speeds on expressways (approximately 60 km/h to 120 km/h), which is consistent with classic pavement dynamic field measurements [28].

The non-monotonic frequency response observed here aligns with the experimental findings of Yue et al. [7], who noted that fatigue life does not decrease with increasing frequency. The peak PWP response at 50 Hz can be explained by the Womersley number (α), which characterizes pulsatile flow in a pipe or pore channel. For a typical pore radius in AC-20 mixture (approximately 0.5 mm, as derived from the gradation in Table 1) and water properties at 25 °C (ν = 1.0 × 10⁻⁶ m²/s), the Womersley number at 50 Hz is calculated using Equation (12).

$$\alpha =R\sqrt{\omega /v}$$

(12)

The calculation yields α ≈ 0.89. This value lies in the transitional regime (0.5 < α < 1.5) where inertial and viscous forces are of comparable magnitude, leading to maximum dynamic amplification and energy dissipation. At lower frequencies (10 Hz, α ≈ 0.4), viscous forces dominate, allowing PWP to dissipate more readily. At higher frequencies (100 Hz, α ≈ 1.3), inertial effects dominate, reducing the fluid’s ability to respond to rapid loading cycles, which limits the build-up of excess PWP. In addition, factors such as material damping, wave attenuation characteristics, and the dynamic response of pore water may also affect the PWP distribution at different frequencies.

As shown in Figure 17, the absolute value of the minimum PWP increased with the increase in loading frequency. This indicates that in the pores of asphalt pavement, the increase in vehicle speed leads to an increase in the absolute value of negative PWP. Therefore, vehicles traveling at high speeds are more likely to cause the stripping and spalling of the asphalt film adhered to the aggregate surface due to adsorption.

3.3. Effect of Loading Frequency on Fatigue Life

Under the load of 700 kPa, time-varying PWP was generated inside the AC-20 model. This pressure couples with stress and affects the contact between particles. Over time, the failure of these contacts leads to particle shedding, as shown in Figure 18.

It can be clearly seen from Figure 18 that under the same load, the damage condition of the model was significantly affected by the loading frequency. When the frequency was 10 Hz, fatigue damage caused seven particles to fall off and 49 cracks to form. When the frequency increased to 50 Hz, the damage was more severe, with 18 particles falling off and 34 cracks forming in the model. When the frequency reached 100 Hz, although only 14 particles fell off, 39 cracks were formed.

Table 3. Fatigue lives at 10 Hz, 50 Hz and 100 Hz.

Load Frequencies (Hz)	Fatigue Lives (h:min:s)
10	114 h 13 min 50 s
50	48 h 16 min 40 s
100	90 h 44 min 22 s

shows the effect of frequency on the fatigue life of the model under the same load.

Table 3 shows that the fatigue life was the shortest at 50 Hz (48 h 16 min 40 s), the longest at 10 Hz (114 h 13 min 50 s), and that the life at 100 Hz was between the two. The fatigue life reduction at 50 Hz (58.1% shorter than under 10 Hz conditions) is comparable in magnitude to the reductions observed in the immersion indirect tensile fatigue tests reported in the previous research [31], in which water-conditioned specimens showed significantly lower fatigue lives than dry specimens. At 50 Hz, the peak PWP reached the maximum (see Figure 16), which weakened the bond strength between aggregates and resulted in the shortest fatigue life. On the contrary, at 10 Hz, the lower peak excess PWP caused less damage to the contact between aggregates, thus leading to a longer fatigue life. For the case of 100 Hz, although the peak excess PWP was also relatively low, the short duration of the load cycle prevented the full development of PWP, resulting in a fatigue life between those at 10 Hz and those at 50 Hz.

3.4. Hysteresis Characteristics Between Load and Maximum PWP

As shown in Figure 19, comparing the time of load application with the time of maximum PWP occurrence indicates that there is a time lag in the PWP response.

The hysteresis characteristic is quantified by the hysteresis angle, the calculation of which is shown in Equation (13):

$$\Phi ={\displaystyle \frac{\mathsf{\Delta }T}{T}}$$

(13)

Table 4. Relationship between frequency and hysteresis angle.

Frequency (Hz)	Lag Angle (°)
10	0.6
50	2.6
100	6.9

shows the hysteresis angles corresponding to different frequencies under the same load amplitude.

As shown in Table 4, the hysteresis angle increased with the increase in loading frequency. Specifically, the hysteresis angle was 0.6° at 10 Hz, rose to 2.6° at 50 Hz, and increased significantly to 6.9° at 100 Hz.

This hysteresis phenomenon can be attributed to the alternating positive and negative seepage processes in the pore structure under alternating loads. To bridge the scale gap between the field pavement structure and the laboratory cylindrical specimen, previous macro-scale Multi-Relaxation-Time Lattice Boltzmann Method (MRT-LBM) dynamic seepage simulations conducted by our research group [24] were introduced for comparative analysis. Although the macro model represents a 60 mm thick field pavement layer under a moving tire (Figure 20) while the current DEM model simulates a laboratory specimen 150 mm in height, both models consistently reveal that the seepage velocity alternates between positive and negative within one loading cycle, with pore water seeping downward to the base course during the compression stage and flowing back upward during the unloading stage. When the frequency increases, the duration of a single cycle is shortened, and the pore water cannot complete a full seepage response cycle, leading to an increase in the phase difference between the pressure response and the load. This cross-scale correlation between mesoscopic seepage and macroscopic hysteresis is the key to understanding the water damage mechanism under high-frequency loads.

Higher loading frequencies shorten the available time for PWP response, leading to an increase in the hysteresis angle. At the low frequency of 10 Hz, the load action time is relatively long, allowing the PWP to respond fully, so the hysteresis angle is small. On the contrary, at the high frequency of 100 Hz, the load action time is extremely short, preventing the full development of PWP and resulting in a significant increase in the hysteresis angle.

4. Conclusions

In this study, a mesomechanical model of saturated AC-20 asphalt mixture considering fluid–solid coupling and damage evolution was established using the PFC2D software, based on the DEM. The effects of load magnitude and loading frequency on the spatiotemporal distribution of excess PWP and fatigue life were systematically investigated, and the mesoscopic mechanism of the load–PWP hysteresis effect was analyzed. The main conclusions are as follows:

(1)

Under cyclic loading, both positive and negative PWPs are generated simultaneously inside the AC-20 model. Positive PWP originates from pore volume compression, while negative PWP (vacuum suction effect) is caused by elastic recovery during unloading. As fatigue damage accumulates, the absolute value of negative PWP continuously increases, indicating expanding regions with vacuum suction effect—a key mesomechanical mechanism of asphalt film stripping.

(2)

The loading frequency exhibits a non-monotonic effect on PWP. At 50 Hz, the maximum positive PWP reaches a peak of approximately 4.6 MPa, while values at 10 Hz and 100 Hz are significantly lower. This 50 Hz peak corresponds to a Womersley number of approximately 0.89, where inertial and viscous forces are comparable, leading to resonant PWP accumulation. Meanwhile, the absolute value of minimum PWP increases with frequency, indicating that high-frequency conditions enhance the vacuum suction effect.

(3)

The fatigue life of the saturated AC-20 model is shortest at 50 Hz (48 h 16 min 40 s), approximately 58% shorter than at 10 Hz (114 h 13 min 50 s). This non-monotonic relationship between frequency and fatigue life is consistent with the frequency–PWP relationship, confirming that excess PWP is a critical factor affecting fatigue performance.

(4)

The PWP response exhibits a clear time lag relative to the applied load, with the hysteresis angle increasing from 0.6° at 10 Hz to 6.9° at 100 Hz. This hysteresis is attributed to alternating positive and negative seepage processes in the pore structure—higher frequencies allow less time for pore water to complete a full seepage response cycle, leading to increasing phase difference.

Mainly based on two-dimensional DEM simulations and qualitative experimental comparisons, this study possesses several limitations. First, the 2D model inherently simplifies pore connectivity and particle interlocking, potentially overestimating PWP values. Second, due to the high computational cost of the fluid–solid coupling algorithm, the particle count was restricted, and thorough sensitivity analyses regarding sample size and void ratio variations were omitted. Finally, damage parameters were primarily calibrated at 25 °C, without fully considering the viscoelastic temperature sensitivity of asphalt. Future research will integrate 3D parallel computing, stochastic modeling, and systematic sensitivity analyses to enhance statistical confidence, while exploring multi-field coupling under unsaturated and variable temperature conditions.