Behaviors of Sediment Particles During Erosion Driven by Turbulent Wave Action

Abstract

Sediment erosion under turbulent wave action is a highly dynamic process shaped by the interaction between wave properties and sediment characteristics. Despite extensive empirical research, the underlying mechanisms of wave-induced erosion remain insufficiently understood, particularly regarding the threshold energy required for particle mobilization and the factors governing displacement patterns. This study employed a custom-built wave flume and a 3D-printed sampler to examine sediment behavior under controlled wave conditions. Rounded glass beads, chosen to eliminate the influence of particle shape, were used as sediment analogs with a similar specific gravity to natural sand. Ten experiments were conducted to systematically assess the effects of particle size, particle number, input voltage (wave power), and water depth on sediment response. The results revealed that (1) only a fraction of particles were mobilized, with the remainder forming stable interlocking structures; (2) the number of displaced particles increased with particle size, particle count, and water depth; (3) a threshold wave power is required to initiate erosion, though buoyancy under shallow conditions reduces this threshold; and (4) wave steepness, rather than voltage or wave height alone, provided the strongest predictor of sediment displacement. These findings highlight the central role of wave steepness in erosion modeling and call for its integration into predictive frameworks. The study concludes with methodological limitations and proposes future research directions, including expanded soil types, large-scale flume testing, and advanced flow field measurements.

1. Introduction

Wave-induced sediment transport plays a critical role in the stability and resilience of hydraulic and coastal infrastructures such as bridges, pipelines, and shoreline defenses [1,2,3,4,5,6,7,8]. Scour evaluation and inspection are essential for both new and existing bridges over waterways to ensure the long-term stability and sustainability of their foundations [9,10]. In lacustrine environments (i.e., lakes and reservoirs), wave-induced erosion can often be the dominant mechanism due to the combination of low current velocities and high wind speeds, which generate relatively large waves. The repeated action of these waves can dislodge and mobilize bed materials, leading to scour around foundations, the exposure of buried structures, and the progressive weakening of protective layers.

Waves arise from wind, vessel traffic, or subsurface disturbances, with wind being the most common driver. Their engineering characteristics—wavelength, height, depth, and period—govern energy transfer and sediment transport (Figure 1) [11]. According to the Coastal Engineering Manual [12], waves may be regular, irregular, non-breaking, or breaking. Regular waves, with uniform height and period, produce predictable impacts, whereas irregular waves introduce complexity through variable flow patterns [13,14]. Wave transformation in shallow waters further alters shape, velocity, and energy distribution, intensifying sediment mobilization [15]. Non-breaking waves generate near-bed oscillatory flows, while breaking waves create strong turbulence that accelerates erosion [16,17].

A distinction must be made between sediment erosion and soil erosion. Natural soils consist of varied particle sizes, mineralogy, organic matter, and cohesion. In contrast, this study examines non-cohesive, granular sediments. To maintain experimental control, uniform glass beads were employed as sediment analogs. These simulate the hydraulic behavior of coarse sands while eliminating the confounding effects of cohesion, angularity, and gradation, thereby enabling clearer analysis of wave-induced particle mobilization.

Wave-induced scour results from interactions between orbital wave motion, the sediment bed, and structural foundations. Numerous studies highlight its importance across coastal, riverine, and reservoir environments. For instance, Douglass and Krolak [18] described that numerous bridge foundations situated in coastal zones, river inlets, lakes, and reservoirs are exposed to the combined effects of waves and currents. Welzel et al. [19] observed greater scour depths at offshore foundations under combined wave–current conditions, particularly on upstream faces. However, most prior work has emphasized current-driven scour, even though wave-only and wave–current mechanisms differ fundamentally [20,21]. Under steady currents, scour is dominated by horseshoe vortices, downflow, vortex shedding, and flow constriction around foundations. In contrast, waves produce oscillatory forcing, repeatedly regenerating these flow features. At small Keulegan–Carpenter (KC) numbers, scour is primarily governed by vortex shedding [22,23,24]. Each shed vortex entrains and removes sediment grains, resulting in net scour over successive wave cycles [22]. The weaker boundary layers associated with wave forcing also limit horseshoe vortex development compared to steady currents [25].

Experimental studies have further revealed distinct scour patterns under wave-only, current-only, and combined forcing (Figure 2) [20]. In wave-only conditions, scour evolves gradually around pile edges; in wave–current conditions, interactions accelerate erosion and deepen scour holes; while in current-only conditions, steady separation and shedding dominate. These insights emphasize that wave-driven erosion produces unique bed morphologies [24,26,27] and that its dynamics are closely linked to KC number and relative current strength [28,29,30]. Importantly, wave-induced local scour can occur on multiple sides of a foundation, unlike current-induced scour, which is typically unidirectional [18].

Despite extensive research on wave-induced scour and sediment transport, several key knowledge gaps remain. First, the threshold conditions for initiating particle mobilization under oscillatory wave action are not yet fully defined. While classical frameworks describe sediment transport under steady currents, the unsteady and cyclic nature of wave force creates more complex initiation dynamics that are not well captured in existing models. Second, the influence of particle-scale properties—such as size, number, and arrangement—and hydrodynamic parameters—such as water depth and wave steepness—on particle displacement patterns has not been systematically quantified. Finally, although classical engineering models such as HEC-18 [9] and the Coastal Engineering Manual (CEM) [12] provide empirical relationships for predicting scour and erosion, they do not explicitly incorporate wave steepness (defined as the ratio of wave height to wavelength) as a governing parameter. This omission is significant, as wave steepness directly reflects wave nonlinearity and has strong physical implications for sediment transport.

To address these gaps, this study employs a custom-designed wave flume and a 3D-printed sampler to examine particle behavior under controlled wave conditions. The main objectives are to

• Investigate particle movement patterns under varying wave conditions in a reproducible laboratory setting.
• Identify the critical thresholds at which particle mobilization occurs, including the role of buoyancy effects under shallow water.
• Demonstrate that wave steepness serves as a more predictive and physically meaningful indicator of sediment mobility than input voltage or wave power alone.
• Provide an experimental dataset that can be used to calibrate and validate advanced computational approaches, such as coupled CFD–DEM simulations, for multiscale modeling of sediment transport.

Through this approach, the study seeks to improve the understanding of wave-induced sediment dynamics, refine predictive frameworks for erosion, and lay the groundwork for integrating laboratory findings into engineering practice. To achieve these objectives, a series of controlled laboratory experiments were conducted using a custom-built wave flume and a 3D-printed sampler, enabling systematic variation in particle properties and wave conditions while directly observing particle displacement and clustering behaviors. By linking microscale particle behavior with macroscale scour mechanisms, this work aims to refine predictive frameworks for wave-induced erosion and contribute to the development of more resilient hydraulic and coastal infrastructure.

2. Methodology

The experiment was carried out in a laboratory-scale wave flume equipped with a custom-designed wave flume and a transparent test section. A 3D-printed soil sampler was integrated into the channel to hold and release particles under wave forcing. Uniform glass beads of varying sizes were used as sediment analogs to ensure experimental repeatability and isolate the effects of particle-scale properties. A series of test cases were designed to systematically vary particle size, particle quantity, input voltage (converted to wave height, wavelength, and steepness through calibration), and water depth. For each test, the number of displaced particles, their travel distances, and offsets from the channel centerline were recorded. Replicate runs were performed to reduce variability and improve statistical reliability. This setup provided a controlled environment to explore threshold conditions for particle mobilization and to evaluate the predictive role of wave steepness in sediment transport.

2.1. Experimental Setup

The experiments were conducted in a laboratory-scale wave flume designed to generate controlled oscillatory flows. The wave flume, powered by a 9–12 V DC supply with a maximum output of 40 W, operated a custom-built paddle driven by an electric motor, enabling precise adjustment of input voltage to regulate wave conditions (Figure 3). The flume measured 1500 mm in length, 50 mm in width, and 190 mm in height, and included a transparent test section to facilitate visual observation and measurement of particle motion. This setup allows for the investigation of various wave properties, including periodic and non-periodic waveforms, wavelength and frequency analysis, phase and group velocities, in-phase and out-of-phase wave superposition, wave reflection, and standing wave formation.

A plastic sampler was fabricated using 3D printing and installed on the channel bed to hold soil analog particles during testing (Figure 4). The sampler was designed with a compartment measuring 25 mm in length, 25 mm in width, and 13 mm in depth, providing consistent initial conditions across test cases. When subjected to wave action, the particles within this compartment were mobilized by the imparted wave energy, enabling direct observation of erosion and transport processes.

To ensure reproducibility and comparability with physical wave parameters, a calibration procedure was conducted to convert input voltage into measurable hydrodynamic quantities, including wave height (H), wavelength (L), wave steepness (H/L), and wave power. Expressing the results in terms of these wave properties, rather than relying solely on device-specific control signals, improved the interpretability of the findings and their reproducibility across facilities. The calibration procedure was suggested by the manufacturer of the wave flume and detailed in the manual.

2.2. Wave Properties

Different input voltages will generate waves with different properties such as wave height, wavelength, wave depth, and wave frequency. Souza et al. [31] proposed the following equation to calculate the wave power for shallow waters:

$$P_w={\displaystyle \frac{1}{8}}{\rho }_{w}g{H}^2\sqrt{gh}$$

(1)

where P_w = wave power; ρ_w = water density, g = gravitational acceleration; H = wave height; and h = wave depth. Please note that “shallow waters” in this experiment refer to a depth-to-wavelength ratio (d/L) less than 0.5, corresponding to the hydraulic shallow-water condition per the Coastal Engineering Manual [12].

To determine the relationship between the input control parameter (voltage) and the corresponding physical wave characteristics, a calibration study was performed using the same experimental setup illustrated in Figure 3. Figure 5 shows the relationship between input voltage and calculated wave power. The results reveal that wave power increases sharply with rising voltage up to a peak value of approximately 9.7 W/m at 8 V, beyond which further increases in voltage lead to a steady decline. This behavior reflects the balance between energy input from the paddle and the onset of dissipative processes such as turbulence, wave breaking, and reflection within the channel. At moderate voltages, energy is efficiently transferred into wave motion, whereas at higher voltages, a larger fraction of the input energy is lost to dissipation rather than contributing to wave propagation. Figure 6 presents the variation in wave height with input voltage. The results indicate that wave height increased rapidly with rising voltage up to a peak value of 0.089 m at 8 V. Beyond this point, further increases in voltage resulted in a gradual decline in wave height. This non-monotonic trend suggests that while moderate voltages effectively transfer energy from the paddle to the water column, higher voltages induce flow instabilities and energy dissipation, leading to a reduction in wave generation efficiency. Such behavior is consistent with laboratory-scale wave generation systems, where turbulence, wave breaking, and reflection effects can dissipate part of the input energy. Figure 7 presents the relationship between input voltage and measured wavelength. The results show a clear inverse trend: as voltage increased, the wavelength decreased steadily, reaching a value of 0.523 m at 8 V. At lower voltages (4–6 V), longer waves were generated, exceeding 1.0 m in length, while higher voltages (10–16 V) produced progressively shorter wavelengths, approaching 0.2 m. This reduction in wavelength with increasing voltage reflects the stronger force of the paddle, which promotes higher-frequency oscillations and shorter wave periods.

The calibration results, including wave height (H), wavelength (L), wave steepness (H/L), and wave power, were subsequently used to interpret sediment transport responses in terms of physically meaningful hydrodynamic parameters rather than device-specific voltage settings. This approach not only ensured that the findings could be generalized and compared with established wave theories and sediment transport frameworks but also highlighted the nonlinear nature of wave generation in laboratory-scale systems, where energy transfer efficiency is influenced by turbulence, dissipation, and reflection effects. Importantly, wavelength, together with wave height, defines wave steepness (H/L), which directly governs the magnitude of orbital velocities near the bed and thus sediment mobilization. By incorporating these parameters into the experimental framework, the study emphasizes the predictive significance of wave steepness and wave power in evaluating sediment mobilization thresholds and transport behavior under controlled oscillatory flows, while improving comparability with established sediment transport models.

2.3. Test Materials

Uniform glass beads were used as sediment analogs in all experiments to simulate soil particles while eliminating the influence of irregular particle shapes, gradation, or cohesion. The beads had diameters ranging from 0.70 mm to 0.90 mm and each individual experiment employed a uniform particle size. The beads had a specific gravity of 2.6, which falls within the typical range for natural coarse sands and offers a reasonable representation of their hydraulic behavior under controlled laboratory conditions. Their smooth, clear-to-white surfaces and an angle of repose of approximately 30° ensured consistent and reproducible behavior under wave forcing. The use of these environmentally friendly, non-cohesive spherical beads enabled the clear isolation of wave–particle interactions under controlled laboratory conditions. However, it is acknowledged that this choice introduces limitations, as natural sediments typically exhibit angularity, gradation, and cohesive forces. These differences are addressed further in the Limitations section.

2.4. Test Plan and Measurements

A total of ten experimental cases were conducted to systematically evaluate the effects of both particle-scale and flow-scale variables. The cases varied in terms of particle size (0.7–0.9 mm diameter), particle quantity (20–100 beads), wave height H, wavelength L, wave steepness H/L, and wave power, and water depth relative to the sampler. The test parameters are summarized in

Table 1. Summary of test cases.

Test No.	Particle Size D (mm)	Number of Particles	Input Voltage (V)	Water Depth d (mm)	Wave Height (mm)	WaveLength (mm)	Frequency	Velocity V m/s	Re	Flow Type	Wave Type	Number of Displaced Particles	Displaced/Total Number of Particles
		N
1 *	0.9	50	8	−6	89	523	1.408	0.736	31,774.5	Turbulence	Regular	12	0.24
2	0.8	50	8	−6	89	523	1.408	0.736	31,774.5	Turbulence	Regular	10	0.2
3	0.7	50	8	−6	89	523	1.408	0.736	31,774.5	Turbulence	Regular	6	0.12
4	0.9	20	8	−6	89	523	1.408	0.736	31,774.5	Turbulence	Regular	5	0.25
5	0.9	100	8	−6	89	523	1.408	0.736	31,774.5	Turbulence	Regular	45	0.45
6	0.9	50	4	−6	25	1046	0.704	0.736	31,774.5	Turbulence	Regular	0	0
7	0.9	50	12	−6	64	309	2.112	0.653	28,158.6	Turbulence	Irregular	33	0.66
8	0.9	50	16	−6	32	186	2.816	0.523	22,601.1	Turbulence	Irregular	17	0.34
9	0.9	50	8	−12	89	523	1.408	0.736	31,774.5	Turbulence	Regular	0	0
10	0.9	50	8	0	89	523	1.408	0.736	31,774.5	Turbulence	Regular	18	0.36

Note: * = baseline case; negative water depth values (–6 mm, –12 mm) indicate that the water level is below the elevation of the particle sampler (located 100 mm above the base of the wave flume). Zero (0 mm) indicates that the water level matches the sampler elevation.

. The relationship shown in Figure 5 was used to control wave power indirectly by adjusting the input voltage.

In each test, particle distribution patterns were evaluated using three primary measurements: (i) travel distance from the sampler along the flat portion of the wave channel floor and does not include the inclined section of the beach slope, (ii) horizontal offset from the channel centerline, and (iii) the total number of particles displaced from the sampler. Measurements were taken once no additional particles were observed to detach from the sampler, ensuring a consistent endpoint across cases.

Each test condition was repeated three times to reduce experimental variability, with the average values reported for analysis. This approach ensured that observed trends in particle mobilization and distribution were representative of the test conditions rather than artifacts of single-run variability. The measurements were taken when no more particles fell off the sampler. The relationship presented in Figure 5 was adopted to control the wave power indirectly by changing the input voltage.

Table 1 summarizes the test conditions used in this study. Particle-scale variables included particle size (0.7–0.9 mm diameter) and particle quantity (20–100 beads), while flow-scale variables included input voltage and water depth relative to the sampler. Each case was designed to isolate the effect of one or more parameters on particle displacement patterns. In Table 1, we also included the wave height, wavelength, frequency, Reynolds number, flow type, and wave type. The Reynolds number is expressed in an open channel flow as

$$R_e={\displaystyle \frac{\rho V{R}_h}{\mu }}$$

(2)

where ρ = fluid density, V = average fluid velocity, R_h = the hydraulic radius defined as the ratio of the cross-sectional flow area A and the wetted perimeter p, and µ = kinematic viscosity. In this study, ρ = 1000 kg/m³, μ = 1.0 × 10⁻³ Pa·s, R_h = 0.04315 m, and V is listed in Table 1.

Open channel flow is typically classified as laminar when Re ≤ 500, turbulent when Re ≥ 2500, and transitional between 500 ≤ Re ≤ 2500. Based on the conditions listed in Table 1, the flow in all test cases is clearly within the turbulent regime.

3. Test Results and Analysis

3.1. Baseline Case

For each test, three measurements were recorded: the travel distance along the wave channel, the horizontal offset from the channel centerline, and the number of particles displaced from the sampler. In the baseline case, 50 particles (particle size 0.9 mm) were initially placed in the sampler, of which only 12 were dislodged by the waves, while the remaining particles remained in place despite repeated wave cycles. The maximum recorded travel distance was 266.7 mm, accompanied by a horizontal offset of 19.1 mm from the channel centerline. This outlier occurred only once among the three replicates, while the other two runs produced consistent results without this anomaly.

Figure 8 illustrates the travel distances and horizontal offsets of the displaced particles. Of the 12 glass beads mobilized, 11 clustered within a range of 70–90 mm from the sampler, while one particle traveled significantly farther. This clustering suggests that the majority of particles were subjected to comparable impulse forces during the initial wave cycle, leading to similar transport distances. The outlier may have been influenced by oscillatory flow near the channel bed at the onset of wave generation. The remaining 38 particles likely stayed within the sampler due to interparticle friction and mechanical interlocking, which contributed to the formation of a stable particle structure.

3.2. Effect of Particle Size

Figure 9 illustrates the influence of particle size on the distribution of displaced particles along the wave channel. In Case 2, with a particle size of 0.8 mm, a total of 10 particles were mobilized from the sampler, whereas in Case 3, with a smaller particle size of 0.7 mm, only 6 particles were displaced. This result indicates that, under identical wave conditions with an input voltage of 8 V, larger particles were more readily dislodged from the sampler. A plausible explanation is that smaller particles exhibit stronger interparticle interactions, such as friction and mechanical interlocking, which enhance their resistance to motion. These effects are closely tied to particle-scale characteristics including the surface area-to-mass ratio, interparticle cohesion, and hydrodynamic drag. Interestingly, once the smaller particles were dislodged, they tended to travel farther along the wave channel, reflecting their lower inertia and greater sensitivity to flow-induced transport. However, as shown in Figure 9, the 0.8 mm particles (Case 2) traveled slightly farther than the 0.7 mm particles (Case 3), indicating that this trend may not be strictly monotonic with particle size. This deviation is likely due to experimental variability and the specific flow conditions at the 8 V input, which may have produced localized turbulence or nonuniform flow patterns affecting particle motion. While smaller particles generally exhibit greater mobility once mobilized, these results highlight the need for additional tests under varying wave conditions to confirm the observed relationship between particle size and travel distance. These findings highlight the importance of considering particle size in predicting sediment mobility under wave forcing.

3.3. Effect of Number of Particles

Figure 10 shows the influence of particle quantity on the distribution of displaced particles. In Case 4, 5 out of 20 particles were mobilized from the sampler, whereas in Case 5, 45 out of 100 particles were displaced. These results indicate that, under an input voltage of 8 V, the number of displaced particles increases with the total number of particles initially present in the sampler. The observed increase in the number of displaced particles with higher particle counts can be attributed to enhanced collective interactions between the wave flow and the particle bed. A larger number of particles provide a greater total surface area exposed to wave-induced shear and pressure fluctuations, increasing the likelihood that individual particles experience sufficient hydrodynamic impulses to overcome interparticle friction and mechanical interlocking. Consequently, as particle count rises, the probability of mobilization also increases, leading to a higher number of displaced particles under identical wave conditions. Most displaced particles were observed within 70–140 mm of the sampler, with only a few traveling farther, suggesting that under a given wave power, particle transport distance follows a predictable range. This observation provides insight into the mechanisms of sediment erosion under oscillatory wave conditions and indicates that particle displacement responds in a threshold-dependent rather than linear manner to wave forcing. This conclusion is supported by the nonlinear relationship observed between wave energy and the number of displaced particles across multiple test cases. As wave power increased, particle mobilization did not rise proportionally but instead occurred abruptly once a critical energy threshold was exceeded. Below this threshold, particles largely remained stable due to interparticle friction and mechanical interlocking, whereas above it, a significant increase in displacement was recorded. This behavior demonstrates that sediment motion under oscillatory waves is primarily governed by the exceedance of a critical hydrodynamic impulse rather than by a continuous linear response to increasing wave energy. While granular soil transport is generally attributed to fluid-induced boundary shear stress [32,33], the localized influence of wave energy on individual particle motion remains insufficiently understood. To address this gap, further investigations are underway using CFD–DEM modeling to resolve the micromechanical effects of local wave energy on soil particle dynamics.

3.4. Effect of Input Voltage and Wave Parameters

Figure 11 shows the effect of input voltage on the distribution of sediment along the wave channel. At the lowest forcing condition (Case 6, V = 4), no particles were displaced, indicating that the applied wave energy was below the threshold required to initiate particle motion. In Case 1 (V = 8), only a few particles were mobilized, and their travel distances were relatively short. In contrast, Case 7 (V = 12) resulted in the largest number of displaced particles (33), most of which clustered within 70–140 mm from the sampler, reflecting strong hydrodynamic forcing and efficient transport. At the highest voltage (Case 8, V = 16), only 17 particles were displaced, and their distribution was more dispersed, with fewer being mobilized overall. This demonstrates the existence of a critical wave power threshold for initiating sediment erosion, while also revealing that the number of displaced particles does not increase proportionally with input voltage. The nonlinear response, with a peak at 12 V, is likely associated with wave breaking and energy dissipation at higher steepness, which reduces the effective energy available for sediment transport.

Figure 12 presents the relationship between input voltage, wave steepness, defined as the ratio of wave height to wavelength, and the number of displaced particles. Both wave steepness and particle displacement increased with voltage up to a critical level, after which a decline was observed. The number of displaced particles was positively correlated with wave steepness, with Case 7 (12 V) showing the greatest displacement, including many particles transported beyond the 70–140 mm range. This indicates that 12 V represents a critical condition for strong hydrodynamic forcing and efficient particle transport. At higher voltages (e.g., 16 V), however, the number of displaced particles decreased despite relatively large wave steepness. This counterintuitive trend can be attributed to wave breaking and the associated energy dissipation processes. Once the wave steepness exceeded a threshold, a portion of the wave energy was dissipated through turbulence, vortical structures, and air entrainment rather than being transmitted directly to the sediment bed. As a result, the effective hydrodynamic stresses acting on the sediment surface were reduced, leading to fewer mobilized particles. This nonlinear response is consistent with prior studies of wave-induced sediment transport, which emphasizes the limiting role of wave breaking in sediment entrainment under strong wave forcing [34,35]. A key finding of this study is that wave steepness provides a more predictive and physically meaningful indicator of sediment erosion than input voltage. While voltage served as the experimental control parameter, it does not directly reflect the hydrodynamic forces acting on sediment. In contrast, wave steepness consistently correlated with particle displacement and clustering, underscoring its value in improving sediment transport models and erosion prediction frameworks.

Figure 13 illustrates the relationship between wave steepness and the number of displaced particles, demonstrating a clear nonlinear trend. At low steepness values (<0.10), particle motion was minimal, with negligible displacement observed. As wave steepness increased beyond approximately 0.15, a sharp rise in particle displacement occurred, indicating the presence of a critical threshold for mobilization. This threshold behavior suggests that orbital velocities induced by waves below this steepness are insufficient to overcome interparticle friction and stability within the sampler, whereas waves exceeding the threshold impart enough hydrodynamic stress to initiate significant erosion and transport. The rapid increase in displaced particles at steepness values between 0.15 and 0.20 highlights the sensitivity of sediment mobilization to small changes in wave steepness once the critical condition is surpassed.

These findings are consistent with the coupled trends observed in Figure 12, where both wave steepness and the number of displaced particles followed similar patterns across different input voltages. Together, the two figures confirm that wave steepness is a more physically meaningful predictor of particle mobilization than input voltage, wave height, or wavelength alone, reinforcing the importance of incorporating steepness into sediment transport and erosion modeling frameworks.

3.5. Effect of Water Depth and Particle Embedment

Figure 14 illustrates the combined effects of sampler embedment depth and water level on the distribution of displaced particles along the wave channel. When the water level was 12 mm below the elevation of the particles in the sampler (Case 9, d = –12 mm), the generated waves consistently reached the sampler compartment during each test; however, no particle movement was observed, indicating that the hydrodynamic force transmitted to the compartment was insufficient to overcome particle stability. In Case 1 (d = –6 mm), only a limited number of particles were displaced, with most clustering within 70–100 mm from the sampler. By contrast, when the water level matched the elevation of the particles (Case 10, d = 0 mm), a total of 18 particles were mobilized, several of which traveled beyond 150 mm from the sampler. These results demonstrate that particle displacement increases with rising water levels and shallower embedment depths. A plausible explanation is that buoyancy reduces effective particle weight, thereby lowering the threshold for initiation of motion. Furthermore, higher water levels and reduced embedment enhance the exposure of sediment particles to wave-induced shear stresses, facilitating both mobilization and longer transport distances.

4. Discussion, Limitations, and Future Directions

4.1. Wave Steepness as a Predictive Indicator

The experimental results provide clear evidence that wave steepness, defined as the ratio of wave height to wavelength (H/L), is a more effective predictor of particle displacement than input voltage, wave height, or wavelength considered independently. Unlike voltage, which serves only as a control variable for wave generation, wave steepness integrates two critical hydrodynamic factors, wave height and wavelength, that more accurately represent the physical forces acting on sediment particles. Steeper waves exert stronger near-bed orbital velocities, imparting sufficient hydrodynamic impulses to overcome particle stability and promote erosion.

This finding aligns with prior studies showing that steeper waves generate stronger erosive forces, contributing to both coastal and bank erosion [36,37,38,39]. Figure 12 and Figure 13 confirm this relationship, with sediment displacement increasing sharply once wave steepness exceeds a threshold of 0.15–0.20. Such nonlinear responses underscore the importance of incorporating steepness into predictive frameworks.

Classical engineering models such as HEC-18 [9] and the Coastal Engineering Manual (CEM) [12] form the foundation of scour and sediment transport prediction, but they emphasize parameters such as mean flow velocity, bed shear stress, or wave height without explicitly incorporating steepness. The present study suggests that wave steepness could complement these models by providing a more integrated descriptor of hydrodynamic forcing. While further work is required to embed steepness directly into engineering design formulas, its demonstrated predictive capacity highlights an opportunity to refine scour and sediment transport models, bridging laboratory observations with established practice.

4.2. Contrast with Shields Parameter Frameworks

Classical sediment transport frameworks, such as those based on the Shields parameter [40], describe incipient motion primarily in terms of bed shear stress under steady flows. While effective in current-dominated environments, these approaches do not fully capture the cyclic and unsteady forcing produced by waves. The present study demonstrates that wave steepness, by integrating wave height and wavelength, offers a more direct measure of the orbital velocities and impulses responsible for sediment mobilization under oscillatory flows. By complementing Shields-based criteria, steepness provides engineers with an additional predictive tool that more accurately reflects the dynamic nature of wave-driven erosion.

4.3. Particle Interlocking and Stability Structures

The results also revealed that a substantial number of particles remained in the sampler even after exposure to multiple wave cycles. This persistence suggests the presence of interparticle friction and “interlocking stability structures” that resisted mobilization. Such macroscopic evidence highlights the stabilizing role of granular arrangements, which reduces susceptibility to displacement despite repeated hydrodynamic forcing.

Although turbulence was not directly measured, the oscillatory flow created sufficient impulses to mobilize particles, while those engaged in stable interlocking remained immobile. This behavior is consistent with prior studies of granular media, where particle friction, collision, and clustering delay the onset of erosion. However, the specific micromechanical mechanisms underlying these observations remain unresolved.

Recent advances in Discrete Element Method (DEM) and Molecular Dynamics (MD) simulations provide powerful tools to capture microscale processes such as contact forces, frictional resistance, and microstructural rearrangements [41]. Integrating such approaches with laboratory-scale experiments could clarify how particle interlocking forms and collapses, bridging the gap between macroscopic erosion patterns and underlying micromechanical drivers. This multiscale framework represents a promising direction for future research.

4.4. Scale Effects and Flow Limitations

As with many laboratory investigations, the experimental design is subject to scale effects and flow limitations. The narrow flume geometry may have amplified wall influences, while the relatively short test durations restricted the ability to observe cumulative erosion under long-term cyclic loading. These conditions constrain the direct extrapolation of results to field-scale environments.

It is acknowledged that the relationship between wave steepness and voltage established in this study is influenced by the geometry and aspect ratio of the experimental basin (1500 mm L × 50 mm W). Variations in basin width, depth, or boundary configuration can affect wave reflection, energy dissipation, and turbulence patterns, potentially altering the precise relationship between input voltage, wave characteristics, and sediment response. While wave steepness is a dimensionless parameter that fundamentally governs the hydrodynamic forcing on sediment particles, its quantitative influence may vary with different flume geometries due to scale and boundary effects. Therefore, the conclusion regarding the critical role of wave steepness in sediment erosion should be interpreted as geometry-dependent, and future studies employing flumes of different dimensions and aspect ratios are needed to validate the universality of this relationship.

The geometry of the box-shaped sampler may have introduced localized hydrodynamic effects that influenced particle motion near its boundaries. The sharp edges of the compartment can generate small-scale turbulence, flow separation, and localized vortices as waves propagate over and around the sampler, potentially affecting the initiation and trajectory of particle movement along the edges. Experimental video observations showed that most particles were mobilized from the central region of the sampler, where the flow was more uniform and less influenced by boundary disturbances, suggesting that edge-induced turbulence was limited but still present. Recognizing this as a potential source of variability, future experiments should consider using modified sampler geometries—such as rounded corners or sloped transitions—to minimize flow disturbance and improve the uniformity of hydrodynamic conditions acting on the particle bed.

Despite these limitations, the experiments provided reproducible insights into wave–particle interactions at controlled scales, supporting the identification of critical thresholds for mobilization. Importantly, buoyancy effects under shallow water conditions reduced the effective particle weight, thereby lowering the erosion threshold. This observation is consistent with previous studies [22,32,42] and highlights the role of water depth in modulating transport behavior.

Future research should address scaling challenges by conducting larger-scale experiments with extended cyclic loading, which would more accurately replicate field conditions and cumulative erosion effects. Coupling laboratory observations with numerical upscaling techniques will also be necessary to establish robust linkages between microscale sediment behavior and macroscale scour development.

4.5. Flow Field Measurements

A key limitation of this study is the absence of direct hydrodynamic measurements. Direct measurements of velocity and turbulence fields were not conducted in this study because the primary objective was to investigate sediment response and displacement behavior under controlled wave conditions rather than to perform detailed hydrodynamic characterization. The experimental setup was therefore optimized for visual observation and particle tracking, with wave properties such as height, wavelength, and steepness derived from calibrated relationships between input voltage and physical wave parameters. Nonetheless, we acknowledge that direct flow measurements would provide valuable quantitative insights into near-bed shear stresses and turbulence structures governing particle mobilization.

To address this gap, future studies should integrate advanced flow diagnostics such as Particle Image Velocimetry (PIV) and Acoustic Doppler Velocimetry (ADV) to capture detailed velocity distributions, turbulence intensities, and near-bed shear stresses. Such measurements would directly link sediment displacement patterns to local flow structures, providing stronger validation for coupled CFD–DEM modeling, which is currently underway to evaluate the effect of localized wave energy on particle motion. This integration of experimental and computational approaches will substantially advance predictive capacity for sediment mobilization under oscillatory flows.

4.6. Link to CFD–DEM Model Validation

The experimental dataset developed in this study, covering particle displacement patterns under controlled variations in wave steepness, water depth, and particle-scale properties, provides a reproducible basis for calibrating and validating coupled CFD–DEM simulations. Such models are increasingly used to resolve wave–particle interactions at the microscale, yet they require robust physical benchmarks to ensure predictive accuracy. By quantifying threshold steepness values for particle mobilization and documenting clustering behavior, the present experiments supply essential inputs for model parameterization and verification. Future work will focus on integrating these datasets into multiscale simulations, enabling stronger linkages between laboratory-scale observations and numerical predictions of sediment transport and scour development.

4.7. Sustainability and Broader Implications

Understanding sediment erosion under dynamic hydraulic conditions is critically important for advancing sustainable development goals (SDGs), particularly those related to resilient infrastructure, sustainable land use, and disaster risk reduction. The identification of wave steepness as a key predictor of sediment response has direct applications for the design and maintenance of coastal and riverine infrastructures, including buried pipelines, coastal defenses, and urban foundations. Improved predictive capability supports proactive adaptation strategies in the face of sea-level rise, storm surge, and extreme weather events.

These findings align with global sustainability priorities, notably SDG 9 (Industry, Innovation, and Infrastructure), SDG 11 (Sustainable Cities and Communities), and SDG 13 (Climate Action) [43]. Moreover, the use of controlled laboratory experiments with reproducible, low-resource methods contributes to sustainable research practices by minimizing environmental impacts. By integrating these findings into engineering practice and policy, erosion risk assessment and mitigation can be improved, promoting long-term resilience and the preservation of natural resources.

4.8. Implications for Engineering Practice

The findings of this study carry direct implications for the design, assessment, and maintenance of hydraulic and coastal infrastructure. By demonstrating that wave steepness is a more reliable predictor of sediment mobilization than conventional parameters such as wave height or wavelength, the results highlight the need to incorporate steepness-based criteria into engineering frameworks.

For bridge foundations, improved prediction of wave-induced scour can enhance inspection protocols and inform the design of protective countermeasures, reducing the risk of structural instability. In shoreline protection and embankment design, integrating wave steepness into erosion models can support more accurate assessments of armor stability and sediment loss, leading to more resilient coastal defenses. For subsurface pipelines and buried utilities, recognition of threshold steepness conditions can aid in the development of burial depth standards and erosion monitoring strategies, particularly in lacustrine or estuarine environments where oscillatory flows dominate.

The identification of wave steepness as a more reliable predictor of sediment mobilization has direct implications for refining existing engineering design standards. Current guidelines, such as HEC-18 and the Coastal Engineering Manual (CEM), emphasize parameters including mean velocity, bed shear stress, or wave height, but they do not explicitly account for wave steepness. Incorporating steepness into these frameworks would provide engineers with a parameter that more directly represents the nonlinear hydrodynamic forcing responsible for scour initiation under oscillatory flows.

For example, threshold steepness values identified in this study (~0.15–0.20) could be incorporated as supplementary design criteria for bridge foundation assessments or shoreline protection strategies, complementing existing shear-based approaches. This integration would improve predictive accuracy for local scour depths, contraction scour, and sediment displacement in environments where wave–current interactions are critical. By bridging laboratory-scale findings with established empirical equations, future versions of HEC-18 and CEM could adopt steepness-based modifiers, thereby enhancing the resilience and sustainability of coastal and hydraulic infrastructure.

The identified threshold wave steepness of approximately 0.15–0.20 represents a preliminary range derived from the specific experimental conditions used in this study. While this value effectively characterizes the onset of significant particle mobilization within the current flume setup, it is recognized that variations in flume geometry, boundary effects, and wave generation mechanisms may influence the exact threshold. Therefore, this range should be interpreted as indicative rather than universal. Further verification through experiments and numerical modeling conducted under different wave conditions, aspect ratios, and basin geometries is necessary to confirm the robustness and general applicability of this critical wave-steepness threshold for predicting sediment erosion behavior.

4.9. Summary of Limitations of the Study

The use of uniform glass beads in this study provided a controlled and repeatable means of isolating the effects of wave-induced hydrodynamic forces on particle motion; however, this material choice also introduces certain limitations. The smooth, spherical geometry and lack of cohesion of glass beads differ from the angularity, sphericity, composition, surface roughness, and cohesive behavior typical of natural sediments [44]. As a result, the threshold for particle mobilization observed in this study may be slightly different than that for natural sands or silts, where interlocking and cohesive forces can modify resistance to motion. Glass beads were intentionally selected to minimize the complexity associated with particle cohesion, allowing the effects of turbulent flow and wave steepness on sediment erosion to be more clearly identified. This simplification has been acknowledged as a limitation, and future work will incorporate natural soils with varying shapes, gradations, and cohesive properties to more accurately capture the erosion thresholds observed in real-world conditions. These simplifications limit direct transferability of the findings to field conditions but offer a useful baseline for isolating particle–wave interactions. Future studies should expand to soils with varying gradation and cohesion to capture a broader spectrum of erosion behaviors.

Second, the laboratory flume was narrow and short, introducing potential wall effects and limiting the ability to simulate large-scale or long-duration cyclic loading. This may underestimate cumulative erosion processes that are critical in real-world environments. Larger-scale facilities and extended tests are needed to validate threshold conditions and capture long-term soil–fluid interactions.

Third, no direct flow field measurements were collected in this study. As a result, turbulence intensity, velocity distributions, and near-bed shear stresses were inferred indirectly from calibration curves rather than measured directly. Future experiments should incorporate flow diagnostics such as PIV and ADV to quantify hydrodynamics and provide stronger validation for coupled CFD–DEM models.

Fourth, the tests represent short-term observations that do not capture progressive or multi-event erosion scenarios, which are common in natural settings. Scaling laboratory findings to field-scale systems remain a challenge due to differences in hydrodynamic forcing, particle properties, and boundary conditions. Bridging this gap will require a multiscale approach combining laboratory experiments, numerical modeling, and field monitoring.

Finally, while macroscopic evidence of particle interlocking and stability structures was observed, the micromechanical mechanisms underlying this phenomenon remain unresolved. Advanced numerical techniques such as DEM and MD simulations should be integrated to explore particle-scale interactions, including frictional resistance, collisions, and microstructural rearrangements, and to link them to observed threshold responses.

Despite these limitations, the study highlights wave steepness as a physically meaningful predictor of particle mobilization, offering a pathway to refine existing scour and sediment transport frameworks. Future work integrating multiscale experiments, direct hydrodynamic measurements, and advanced simulations will further enhance predictive capacity, enabling more robust design and maintenance strategies for resilient infrastructure under wave-induced erosion.

4.10. Suggested Future Research Directions

Based on the findings and limitations of this study, several avenues for future research are recommended:

(1)

Particle-Scale Mechanisms

• Apply Discrete Element Method (DEM) and Molecular Dynamics (MD) simulations to investigate micromechanical processes such as interlocking, collisions, and frictional resistance.
• Explore the formation and collapse of “particle stability structures” to better explain threshold behaviors observed in the experiments.

(2)

Hydrodynamic Field Measurements

• Integrate advanced diagnostics such as Particle Image Velocimetry (PIV) and Acoustic Doppler Velocimetry (ADV) in wave flume experiments to capture velocity distributions, turbulence intensities, and near-bed shear stresses.
• Link measured flow fields directly to sediment mobilization patterns for stronger model validation.

(3)

Scaling and Long-Term Effects

• Conduct larger-scale flume experiments to reduce wall effects and improve representativeness of field conditions.
• Extend testing to include long-duration cyclic loading and multi-event erosion scenarios to capture cumulative soil displacement processes.

(4)

Diverse Sediment Types

• Future research should expand the experiments to include natural soils that exhibit gradation, angularity, and cohesion to complement the simplified glass bead tests. Incorporating mixtures of particle sizes will provide valuable insights into interparticle interactions, packing effects, and differential mobilization behavior under oscillatory wave conditions. Such studies would better capture the complexity of natural sediment beds and improve the applicability of laboratory findings to real-world erosion and sediment transport processes.
• Compare results across sediment types to refine threshold criteria for erosion under oscillatory flows.

(5)

Integration into Engineering Models

• Couple wave steepness as a predictive parameter into classical frameworks such as HEC-18 and the Coastal Engineering Manual (CEM).
• Develop hybrid predictive tools that combine laboratory-derived steepness thresholds with established engineering equations for scour and sediment transport.

(6)

Sustainability and Field Applications

• Apply insights to real-world infrastructure, including bridges, pipelines, and coastal defenses, particularly in regions vulnerable to storm surge and sea-level rise.
• Align future work with sustainable development goals (SDGs) on resilient infrastructure, sustainable cities, and climate adaptation.

5. Conclusions

Extensive research has been conducted on wave-induced sediment erosion using empirical approaches. However, the underlying mechanisms remain unclear, particularly regarding the wave power required to initiate erosion, the movement patterns of eroded particles, and the key influencing variables. In this study, a custom-made wave flume and a 3D-printed sediment sampler were employed to investigate sediment dynamics under varying wave conditions. Rounded glass beads, chosen for their similar specific gravity to natural sand and to eliminate the influence of particle shape, served as sediment analogs. The experiments systematically examined the effects of particle size, particle quantity, input voltage (i.e., wave power), and water depth. Based on the results, the following conclusions can be drawn:

(1)

Only a portion of the particles were displaced from the sampler by waves, while the remaining particles formed a stable structure due to interparticle friction and mechanical interlocking.

(2)

The number of displaced particles increased with particle size, particle count, and water depth, highlighting the combined role of particle-scale and flow-scale factors.

(3)

A threshold wave power is necessary to initiate sediment erosion, though buoyancy under shallow conditions significantly lowers this threshold by reducing effective particle stability.

(4)

Particle displacement initiation was found to correlate more strongly with wave steepness than with wave power, input voltage, or wave height alone, making wave steepness a more physically meaningful predictor of erosion potential.

These findings underscore that wave-induced erosion is not a uniform process, but a threshold-driven phenomenon shaped by both hydrodynamic forcing and particle interactions. Incorporating wave steepness into predictive frameworks can improve the accuracy of scour and erosion assessments for coastal and hydraulic infrastructure. While this study provides new insights, limitations include the use of simplified sediment analogs, laboratory scale effects, and the absence of direct hydrodynamic field measurements. Addressing these gaps through multiscale experiments, advanced flow diagnostics, and coupled CFD–DEM modeling will enhance predictive capability. Ultimately, the results offer both theoretical advances and practical implications for infrastructure resilience and sustainability in environments subject to wave-driven erosion.