Experiment on streambed armoring with clusters and its influence on bed-load dynamics

Understanding bed-load transport under various flow conditions is essential for addressing a wide range of issues, including river morphology (Hill et al. 2010), pollutant transport (Jiang et al. 2022), and the evolution of microbial and benthic communities (Duan et al. 2009; Wu et al. 2024). Streambeds with poorly sorted sediment mixtures often develop an armored surface layer featuring various microstructures, such as clusters (Strom et al. 2004), stone cells (Hassan & Church 2000), and flow belts (Sun et al. 2015). These structures influence the local turbulence, near-bed flow velocities, pressure gradients, sediment availability, and transport rates (Brayshaw 1984; Nikora et al. 1998; Hassan & Church 2000; Tan & Curran 2012; Heays et al. 2014; Wu & Singh 2024). Accurately characterizing bed-load dynamics over an armored streambed with clusters remains a significant challenge for river scientists and engineers.

Surface structures emerge from particle interactions and arrangements, influencing bed topography and surface roughness, both of which may affect sediment transport. Although there is a substantial body of research on the dynamic evolution of cluster formation and disintegration, controversy remains regarding the impact of cluster structures on bed stability and bed-load transport. Some studies suggest that clusters may enhance bed stability (Brayshaw 1984), while others argue that under high flow conditions, the disintegration of particle clusters can trigger the destabilization of additional clusters, potentially undermining overall bed stability (Strom et al. 2004; Heays et al. 2014). Mechanisms by which cluster structures influence sediment particle transport vary among studies. Several investigations propose that cluster structures indirectly affect bed-load transport through complex pathways. For example, particle motion characteristics are contingent upon the flow conditions (Wu et al. 2020), with cluster structures capable of altering bed microstructure, thereby impacting near-bed flow velocities and sediment availability (Brayshaw 1984; Papanicolaou & Schuyler 2003; Tan & Curran 2012). Another body of research suggests that particles within clusters actively contribute to bed-load transport (Heyman et al. 2014; Fan et al. 2023). For instance, the disintegration of the clusters, following the entrainment of a group of sheltered small particle entrains, may contribute to a short-term change in bed-load transport rate (Fan et al. 2023). Despite substantial academic efforts, the intricate interplay between the riverbed, near-bed flow, and bed-load transport continues to present significant challenges in forecasting bed-load transport over armored streambeds.

Proper parameterization of the surface cluster pattern is a major challenge in determining the impact of the armored bed on the bed-load transport rate (Zhang et al. 2021). Researchers have attempted to characterize the morphological properties of microforms using various attributes, such as bed surface texture (represented by particle sizes) (Hassan & Church 2000; Wittenberg & Newson 2005) and geometric properties of clusters (e.g., cluster size, horizontal spacing, and bed area coverage) (Papanicolaou & Schuyler 2003; Heays et al. 2014). Additionally, more delicate spatial functions, such as two-dimensional autocorrelation functions (Marion et al. 2003), fractal dimensions (Papanicolaou et al. 2012), and wavelet transforms (Adams 2020), have been employed to describe the spatial distribution of bed microtopography, though these functions were somewhat unintuitive to interpret. More recently, the nearest-neighbor approach, initially popularized in forestry studies, has been proposed to quantify particle aggregation (L'Amoreaux & Gibson 2013), and some researchers have applied it to examine the correlation between surface microforms and hydraulic roughness or bed-load transport rate (Johnson 2017; Zhang et al. 2021). However, these studies did not account for variations in particle diameter, potentially leading to inaccuracies in distinguishing adjacent particles. This limitation compromises the accuracy of surface cluster microform characterization.

Considerable field and laboratory efforts have advanced our understanding of cluster structures and their interactions with flow conditions and sediment supply (Hassan & Church 2000; Strom et al. 2004; Heays et al. 2014). However, field research is often limited by the practicality of continuously monitoring bed conditions and recording cluster behavior during flood events (Wittenberg & Newson 2005). Laboratory clusters using idealized particles, such as glass spheres, overlook the effects of natural variations in particle size and shape found in rivers (Papanicolaou & Schuyler 2003). Recently, several researchers have sought to replicate the complexity of natural bed armoring processes through laboratory experiments, employing image processing techniques to monitor cluster development and sediment movement over extended periods (Heays et al. 2014; Hassan et al. 2020; Singh et al. 2023). Despite these advancements, precise definitions and classifications of clusters remain debated (Brayshaw 1985; Strom et al. 2004; Wittenberg & Newson 2005; Strom & Papanicolaou 2008). In this study, we define a ‘cluster’ following Zhang et al. (2021) as any organization or grouping of sediment particles that is significantly denser than a random particle distribution.

In this study, we conducted a flume experiment using quartz sand designed to replicate the grain size distribution of natural bed sediment. A camera was employed to continuously record the bed surface evolution. The primary objective of this research was to investigate the spatial and temporal evolution of clusters in bed armoring and to explore their effects on bed-load transport. We provide a brief overview of the experimental setup and procedures, the image processing techniques employed, and the methods used to calculate particle spatial patterns. Subsequently, we illustrate the evolution of the clusters using plan-view video and quantify the degree of surface coarsening and particle clustering with two parameters.

The sediment blend incorporated particles from five distinct size categories, with a particle size distribution characterized by D₁₀ = 0.82 mm, D₅₀ = 4.0 mm, D₇₅ = 9.0 mm, and D₉₀ = 13.1 mm, as detailed in Table 1. The mixture was selected based on sediment data from the Lujiahe Site, located along the middle reaches of the Yangtze River in China, an area known for pronounced bed armoring. Sediment was trapped at the flume outlet using a slot. A digital camcorder was mounted above the monitoring area (520 mm × 480 mm) to record the bed surface at 25 frames/s, with a resolution of 1,300 × 1,200 pixels. To mitigate image distortion caused by water surface oscillations, a glass sheet was placed over the water surface.

Prior to initiating the experiment, the sediment bed was leveled, and a low flow of 80 L/s was introduced to minimize disturbance to the bed surface. Throughout the experiment, the bed slope was maintained at 4.2‰, with a tailgate employed to ensure uniform flow along the channel. The discharge was gradually increased from 80 to 150 L/s (refer to Table 2 for relevant hydraulic parameters) to preserve the integrity of the bed structure. To maintain a steady and uniform flow during each discharge phase, the tailgate was precisely adjusted.

Table 2

Hydraulic parameters of the experiment

Q (L/s) .	J (‰) .	h (cm) .	(m/s) .	.	Du (h) .
80	4.2	10.5	0.066	0.751	1.82
85	4.2	10.5	0.066	0.808	1.55
90	4.2	11.0	0.067	0.799	1.55
95	4.2	11.0	0.067	0.832	3.75
100	4.2	11.5	0.069	0.666	1.27
105	4.2	12.5	0.072	0.766	1.07
110	4.2	12.5	0.072	0.808	0.50
115	4.2	13.0	0.073	0.784	0.50
120	4.2	13.5	0.075	0.773	1.28
125	4.2	13.5	0.075	0.811	0.72
130	4.2	13.5	0.075	0.844	0.50
135	4.2	14.0	0.076	0.822	0.50
140	4.2	14.5	0.077	0.810	0.50
145	4.2	15.0	0.079	0.808	0.50
150	4.2	15.5	0.08	0.799	32.43

Q (L/s) .	J (‰) .	h (cm) .	(m/s) .	.	Du (h) .
80	4.2	10.5	0.066	0.751	1.82
85	4.2	10.5	0.066	0.808	1.55
90	4.2	11.0	0.067	0.799	1.55
95	4.2	11.0	0.067	0.832	3.75
100	4.2	11.5	0.069	0.666	1.27
105	4.2	12.5	0.072	0.766	1.07
110	4.2	12.5	0.072	0.808	0.50
115	4.2	13.0	0.073	0.784	0.50
120	4.2	13.5	0.075	0.773	1.28
125	4.2	13.5	0.075	0.811	0.72
130	4.2	13.5	0.075	0.844	0.50
135	4.2	14.0	0.076	0.822	0.50
140	4.2	14.5	0.077	0.810	0.50
145	4.2	15.0	0.079	0.808	0.50
150	4.2	15.5	0.08	0.799	32.43

Note. The friction velocity, is calculated as ⁠, where J is the slope of the bed surface, h is the average flow depth. The Froude number ⁠, is defined as ⁠, where represents the mean bulk fluid velocity. Q is the volumetric discharge, and A is the cross-sectional flow area. The duration of each discharge is denoted by Du.

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In this study, the criterion for a stable armor layer was defined as the point at which the majority of the largest-size group particles (Group 5) remained stationary for an extended period of time, i.e., 2 min. To reduce subjectivity, a single observer assessed the stability of the armor layer throughout the experiment. Moving particles were collected at the flume outlet every 15 min and subsequently weighed. An insignificant part of the trapped particles was sampled, dried, sieved, and weighed to determine their size distribution. Concurrently, the particles were continuously fed into the flume to develop an armored streambed with clusters. The volume of sediment fed was adjusted based on the quantity of sediment collected at the outlet over the previous 15-min interval.

A digital camcorder recorded the entire bed surface evolution. After approximately 36 h, a stable armored bed surface was established over the experimental section, as evidenced by the sediment transport rate stabilizing at an average value of 4.59 g/s for 12.38 h.

Clusters within the surface layer are composed of interlocking clasts that form around notably large bed particles, which protrude slightly above otherwise planar gravel beds (Brayshaw 1985). These microforms may appear as discrete structures or as interconnected networks of grouped particles (Strom et al. 2004). The present study focuses on the largest-size group of particles (hereinafter referred to as ‘key particles’) as the primary indicator of bed evolution. For ease of image processing, these key particles were pre-colored yellow. The bed surface was continuously monitored throughout the experiment to investigate the spatial evolution of sediment clusters.

Second, distinct from traditional ecological applications, this study emphasizes the temporal dynamics of particle clustering on the bed surface. An I value is assigned to the bed surface at each specific time t throughout its evolution. For example, at t = 1 h (Figure 3(b)), the -matrix yields u₁₂ = 0, u₁₃ = 1, u₁₄ = 0, u₁₅ = 0, and u₁₆ = 0. Summing these values results in I = 6 at t = 1 h. Similarly, at t = 2 h (Figure 3(c)), I rises to 10, and at t = 3 h (Figure 3(d)), I reaches 16.

By analyzing the video footage captured of the bed surface, we obtained a series of values over the bed armoring process using the aforementioned image processing techniques and in accordance with Equations (5)–(7).

Natural bed clusters within a stable armored bed form through ‘self-organized’ driven by variations in flow and sediment conditions (Wittenberg & Newson 2005). These clusters can be categorized into five distinct shapes: pebbles, heaps, comets, lines, and ring-shaped, as described by Strom & Papanicolaou (2008). Our experimental observations documented the dynamic transformation of the sediment bed over time, transitioning from an initially uniform and smooth surface to a more rugged one, characterized by the development of particle clusters. Throughout the experiment, we observed all five of the cluster shapes mentioned above, and their corresponding plan-view sketches and laboratory photographs are comprehensively presented in Table 3.

Table 3

Various shapes of clusters on the experiment bed surface (after Strom & Papanicolaou 2008)

Shape .	Plan-view sketch .	Laboratory photograph .	Shape .	Plan-view sketch .	Laboratory photograph .
Pebble			Heap
Comet			Line
Ring

Shape .	Plan-view sketch .	Laboratory photograph .	Shape .	Plan-view sketch .	Laboratory photograph .
Pebble			Heap
Comet			Line
Ring

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Throughout the experiment, as flow continuously interacted with the bed, the proportions of the five cluster types varied across different stages of bed evolution. Initially, the bed was dominated by individual pebble and heap-shaped clusters. Over time; however, these clusters began to merge into more complex, interlocking structures comprising multiple shapes. Notably, even within what appeared to be an armored bed under constant inflow, certain clusters exhibited dynamic rather than static behavior. These clusters would collapse under near-bed turbulent surges, only to rapidly reform a short distance downstream.

In the previous subsection, we provided a qualitative characterization of the evolving patterns of particle configurations based on visual observations. In this section, we proceed with a quantitative analysis of bed surface evolution, utilizing the metrics Rn(t) and as defined in the ‘Experimental Techniques and Methodology’ section.

The bed surface clustering metric, denoted as ⁠, shows minimal variation during the initial phase of increasing flow. However, after the discharge stabilizes at 150 L/s, experiences an increase, followed by a decline, which is attributed to the self-organization of the armored bed surface. This non-monotonic trend in variations aligns with the patterns previously outlined by Zhang et al. (2021). By examining the temporal progression of both Rn and ⁠, it is evident that bed surface coarsening and particle clustering can indeed occur concurrently. Initially, bed coarsening dominated the process, but in the later stages, the focus shifted to changes in the bed's microstructure, with the adjustment of particle clustering becoming more prominent.

Several representative moments, marked by the red hollow points in Figure 4, were selected at random from the bed evolution process. Details of these snapshots, along with key parameters and general observations of the bed surface, are compiled in Table 4. Initially, the bed surface was primarily covered with fine to medium-sized particles, with key particles dispersed randomly. As the discharge gradually increased, particles began to aggregate into small clusters, typically consisting of 4–8 key particles, along with a number of smaller particles. However, most of these clusters were short-lived due to flow turbulence. Over time, the proportion of key particles within the bed surface increased. With the discharge rising from 90 to 150 L/s, the clusters grew in size over time to withstand the increasing hydraulic forces, displaying diverse shapes such as pebbles, lines, and heaps. In the following phase, as discharge stabilized at 150 L/s, the proportion of the bed surface occupied by key particles remained relatively constant, while the particle clustering parameter initially increased and then decreased as time progressed.

Table 4

Evolution process of the coarsening bed surface (after Zhu 2021)

.	Extraction of snapshot .	Status parameters .	Observation of the bed surface .
①		t = 0.72 h; Rn = 28.15%;	Key particles were approximately randomly distributed The majority of particles were scattered individually
②		t = 4.40 h; Rn = 39.16%;	The percentage of key particle areas increased over time Key particles agglomerated into clusters, with their size expanding as time progressed Fine particles were distributed across the bed surface and sheltered by key particles The dominant types of clusters changed from pebbles and linear structures to heaps and rings
③		t= 33.27 h; Rn = 38.40%;	Percentage of key particle areas approached a stable state Medium-sized clusters scattered throughout the bed grew into large clusters (>15 key particles) Large clusters were composed of multiple sub-clusters, each exhibiting various shapes
④		t = 47.73 h; Rn = 45.75%;	The percentage of key particle areas exhibited minimal change as time progressed The bed surface became increasingly covered by complex structures of clusters in various shapes and sizes Flow belts, marked by blue dashed lines, developed between clusters, along the flow direction

.	Extraction of snapshot .	Status parameters .	Observation of the bed surface .
①		t = 0.72 h; Rn = 28.15%;	Key particles were approximately randomly distributed The majority of particles were scattered individually
②		t = 4.40 h; Rn = 39.16%;	The percentage of key particle areas increased over time Key particles agglomerated into clusters, with their size expanding as time progressed Fine particles were distributed across the bed surface and sheltered by key particles The dominant types of clusters changed from pebbles and linear structures to heaps and rings
③		t= 33.27 h; Rn = 38.40%;	Percentage of key particle areas approached a stable state Medium-sized clusters scattered throughout the bed grew into large clusters (>15 key particles) Large clusters were composed of multiple sub-clusters, each exhibiting various shapes
④		t = 47.73 h; Rn = 45.75%;	The percentage of key particle areas exhibited minimal change as time progressed The bed surface became increasingly covered by complex structures of clusters in various shapes and sizes Flow belts, marked by blue dashed lines, developed between clusters, along the flow direction

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In the initial phase of the 150 L/s stage, medium-sized clusters (comprising 9–15 key particles) coalesced into larger assemblies (>15 key particles), which consisted of diverse sub-cluster shapes closely packed together. As the experiment progressed, the effect of these clusters on near-bed turbulence became more pronounced with their continued growth. This blocking effect, in turn, generated near-bed turbulence, which played a significant role in the evolution of the armored bed surface. Specifically, key particles within the large clusters were entrained and carried away by evolving coherent flow structures, resulting in the gradual formation of flow belts between the clusters (indicated in Table 4; ④). As reported by Sun et al. (2015), these belts act as channels that facilitate the rapid transport of fine particles. As a result, during the later stages at 150 L/s, the degree of particle clustering gradually decreased. After an extended period of mutual adjustment between the bed structure and the near-bed turbulence, the bed surface evolved into a complex structure characterized by clusters of varying sizes and shapes, interspersed with flow belts. By this stage, the bed surface had reached a dynamic equilibrium, adapting to the hydrodynamic conditions at 150 L/s, with the bed coarsening (Rn) and particle clustering parameters fluctuating within a stable range.

Building upon the data from the experimental inflow discharge and the variations in two key bed quantitative parameters, we have categorized the evolution of the experimental bed surface structure into four periods. These periods, labeled P1–P4, are demarcated by red dotted lines in Figure 4 and include: (1) bed coarsening, (2) emergence of prototype clusters, (3) interconnection of neighboring clusters, and (4) formation of mature clusters with high flow belts.

Figure 5 reveals that both formulas are inadequate in accurately capturing the bed-load transport rate during the bed armoring process in this experiment. Specifically, the Meyer-Peter formula significantly overestimates the transport intensity throughout the entire process. In comparison, the Wilcock equation provides a closer match to the measurements during P1 to P2. However, it still fails to capture the non-monotonic variation of measured transport rates when the discharge remains constant from P3 to P4. The results indicate that while the Wilcock equation accounts for the variations of the bed surface particle size distribution, which is conceptually similar to the degree of bed coarsening (Rn), it falls short in accurately predicting the bed-load transport rate during phases primarily influenced by particle clustering. To further investigate, we explored the contributions of bed coarsening and particle clustering, indexed by the Rn and ⁠, respectively, to the bed-load transport intensity at various stages of the bed armoring process. The discrepancy (Δq₁=q_MP–q_WC) between the predictions of the Meyer-Peter and Wilcock formulas serves as an indicator of the impact of bed coarsening on bed-load transport intensity, while the variances (Δq₂=q_WC–q_m) between the Wilcock equation's predictions and the measurements reflect the contribution of particle clustering.

Research has examined the dynamics of particle clusters through a series of laboratory studies (Papanicolaou & Schuyler 2003; Heays et al. 2014; Johnson 2017) and field observations (Wittenberg & Newson 2005). Wittenberg & Newson (2005) identified four key processes that characterize alterations in the spatial and temporal patterns of riverbed structures: (a) scouring and removal of cluster particles, (b) aggregation of particles due to deposition processes, (c) in situ modifications, and (d) formation of new bedforms. Hassan et al. (2020) observed in their flume experiments that, following the initial phase of bed surface coarsening, particle structures undergo a sequence of events, including formation, expansion, or contraction, and ultimately fade away. Despite notable, remarkable differences in flow discharge and sediment composition, the evolutionary patterns observed in these investigations were consistent with those identified in the present experimental setup.

To better understand the impact of bed microstructure on bed-load transport, two parameters based on key particle group characteristics were introduced to characterize the bed surface evolution, with Rn representing bed coarsening and indicating particle clustering. The experimental results demonstrate that both bed coarsening and particle clustering reduce the transport intensity of bed load, with the obstructive effect increasing as either Rn or increases. Although several researchers have employed similar parameters to quantify particle clustering (Johnson 2017; Zhang et al. 2021), these parameters typically treat particles as dimensionless points in characterizing their spatial distribution. However, some researchers argue that the dimensions and morphology of objects should be considered when examining their spatial patterns (Wiegand et al. 2006). In our analysis, we conceptualized the key particles as circles with varying diameters, rather than simplifying them to dimensionless points. This method reduces the risk of misclassifying contiguous particles, thereby mitigating the underestimation of particle clustering intensity.

These findings contribute to a deeper understanding of the evolutionary patterns of bed structures and their impact on the movement of bed-load particles. However, several limitations exist within the scope of this study. First, all previous investigations have relied on top-down planar bed images, a method that has been largely dictated by the challenges in obtaining detailed subaqueous three-dimensional (3D) topographical information. Notably, the experimental bed surface underwent a progressive transformation from an initially two-dimensional (2D) plane to a 3D landscape characterized by microstructural features. Recent research by Singh et al. (2023) suggests that the entrapment of bedforms is directly proportional to the ratio of bedform height to particle diameter. As such, the influence of bed surface topography on bed-load transport cannot be overlooked. Future studies should prioritize the development of advanced technological approaches capable of enabling continuous and real-time monitoring of bed surface elevations. Second, Wittenberg (2002) proposed that the particle size distribution plays a pivotal role in the self-formation of clusters. However, this investigation focused solely on the largest fraction of particles to characterize the evolutionary patterns of bed armoring associated with cluster development. Although the qualitative effects of bed coarsening and particle clustering on bed-load dynamics have been outlined, determining a precise mathematical function to describe these processes remains an unresolved issue. Subsequent research endeavors should strive to incorporate a comprehensive analysis of particle size distribution, which would refine the parameters associated with bed armoring. Moreover, these studies should explore the generalized functional relationships between these parameters and the rate of bed-load transport. Finally, the value exhibits an initial increase, followed by a decrease, as the discharge is maintained constant in our experimental setup. This trend was interpreted as reflecting a transformation of the bed surface, where the growth of large clusters gives way to the formation of flow belts. Nevertheless, pinpointing the exact value and timing of this transition requires a more rigorous and in-depth investigation.

The study, which investigates bed surface coarsening and particle clustering using colored particle tracers and image analysis, enhances our understanding of the correlations between bed armoring and bed-load transport. The key findings and conclusions are as follows:

• 1. The experimental monitoring successfully captured the evolution of bed microstructure, with the shapes of particle clusters aligning closely with those described by Strom & Papanicolaou (2008). The evolutionary trajectory of individual particle clusters exhibited patterns similar to those documented in previous field observations and laboratory studies. An important advancement of this study is categorizing the bed armoring process in this experiment into four distinct phases: (1) bed coarsening, (2) emergence of prototype clusters, (3) interconnection of neighboring clusters, and (4) formation of mature clusters with high flow belts.

• 2. Two parameters, Rn and ⁠, based on key particle group characteristics, were used to assess bed coarsening and particle clustering, respectively. This approach provided a more nuanced view of the bed surface evolution. The calculation method for was refined by incorporating the diameters of key particles, reducing the likelihood of misclassifying contiguous particles. Over the course of the bed armoring process, as discharge increased incrementally from 80 to 150 L/m³, Rn values progressively increased. When discharge was maintained at 150 L/m³, values initially rose, then decreased, and eventually stabilized within a certain range. Nonetheless, the peak values and the timing of their occurrence for these two parameters require further investigation.

• 3. The key particles (referring to the largest size group of particles in this study) play a crucial role in the processes of bed surface armoring and bed-load transport. As the discharge gradually increased (P1–P2), the bed coarsening process governed the evolution of the bed surface. With the intensification of bed layer coarsening (i.e., the increased proportion of key particle areas), the inhibitory effect on bed-load transport also strengthened. In the subsequent phases, when the flow was maintained at a higher level (P3–P4), the bed surface structure was primarily reshaped by the self-organization mechanisms of the bed surface. During this process, particle clustering (i.e., the elevated aggregation of key particles) played a significant role in obstructing bed-load transport, and the impact became more pronounced as the degree of particle clustering intensified.

To delve more profoundly into the interplay between bed surface evolution and bed-load transport, it is essential to develop advanced photogrammetric techniques capable of capturing the intricate underwater microtopographies within a controlled laboratory flume. The variability in flow conditions and surface particle size distributions gives rise to a range of morphological patterns, each exerting a distinct impact on the dynamics of bed-load transport. A precise quantification of these effects is a fundamental focus for future academic research in this field.

This study was funded by the National Key R&D Program of China (No. 2023YFC3206201), the National Natural Science Foundation of China (No. U2243219, U2243221, 52279077, and 52109086), the Special Project of Basic Scientific Research Business Expenses of Central Public Welfare Research Institutes (No. HKY-JBYW-2023-21), the Science and Technology Development Foundation of Yellow River Institute of Hydraulic Research (No. HKF202203), and Sichuan Science and Technology Program (2023NSFSC1989). The authors thank the anonymous reviewers for their valuable comments.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.