Self-adjustment mechanism of bed structures under hydrology and sediment regimes

This relation indicates that the average elevation loss due to steps is about 1 to 2 times as big as that due to the gradient. Experimental results of Wang et al. (2004) showed that the Manning's roughness coefficient n linearly increases with the scale of the bed structures.

Generally, bed structures are relatively stable under flow scouring and channel incision (Abrahams et al. 1995; Yu et al. 2008). They can reduce the lift and drag forces acting on the particles on the lee side of the structures (Reid 1992; Yang et al. 2006). Sear (1996) found that clusters on a gravel riverbed are usually very resistant to entrainment. The shear stress required to entrain clustered sediments is higher than that required to entrain dispersed bed particles (Hassan & Church 2000). Therefore, bed structures are sometimes used as stable habitats in ecological restoration projects (Yu et al. 2010, 2012a).

Some of the results cited above are mainly applicable locally due to restricted hydrology and sediment regimes. There were few past studies which could simulate the natural evolution process of bed structures due to limited conditions in the laboratory. A systematic study of bed structures is still required in order to reveal the essential mechanisms, which have been implied in previous valuable work. In order to analyze the distribution and evolution of bed structures under different conditions, as well as the underlying mechanism of fluvial morphology, several field investigations were carried out during this study and an experiment was designed and conducted in a natural river valley.

The annual precipitation in the Diaoga River basin is about 1,000 mm, 2/3 of which concentrates during the flood season (June-September), leading to frequent rainstorms. The daily precipitation reached 35–55 mm on 2006/7/18, 2006/8/11, 2007/7/19 and 2007/8/11 during our investigation. Sometimes, flash floods or even debris flows occurred during these heavy storm events.

Frequent floods have caused the river basin to be incised by many ravines and gullies, most of which are located on the left bank (Figure 3). The Diaoga River basin was once covered by vast vegetation. However, in recent years, human activities including road construction, mining, and farm reclamation have severely destroyed the vegetation, resulting in intensive erosion and sediment-yielding in some gullies (mainly on the left bank).

The Jiangjiagou Ravine is another tributary of the Xiaojiang River (Figure 3). This ravine is known as a natural museum of debris flows. Over many years, the valley's bottom has been filled with layers of debris flow deposits. The poorly sorted deposits can provide various sediment resources (from clay to boulders) for the development of bed structures, forming an ideal place for the field experiment examining bed structure evolution and distribution. In this experiment, the surface of the deposits layer was assumed to be the original land surface without hydraulic erosion. Water and sediment were diverted onto the surface for river simulation so that free degradation, aggradation, and bed structures evolution could be observed.

The distribution of bed structures in the main stream and several large tributaries of the Diaoga River were recorded and summarized in Table 3. The river sections in the same ravine are numbered from upstream to downstream as A, B,C, etc. Channel gradients at the corresponding sections are also included in this table.

The statistics of the data in Table 3 are summarized in Table 4. It can be concluded that the sizes of bed structures increase as the channel gradient increases. Larger bed structures generally occur in higher gradient channels. After long-term fluvial morphology, most channels have adjusted to relatively stable conditions, which demonstrates that larger structures can protect the riverbed and in turn sustain channels with higher gradients. The only exception to this rule is the ‘Others’ structures in the river source, where high gradient (around 0.4) is paired with small grain size (D₉₀: 20 cm). Table 4 also shows that the type of structures have some influences. For example, the grain size of large step-pools and boulder cascade are similar (D₉₀: 50–150 cm), but the channel gradient they can sustain are very different (Large step-pools: 0.15–0.30, Boulder cascade: 0.30–0.50).

The non-bedload scheme was run after the bedload scheme in phase 2 and phase 3 (Table 2). The longitudinal profiles of channels after scouring of relatively clean water changed significantly (Figure 8) due to severe incision. In phase 2, the thalweg elevation was lowered by 0.2 to 0.5 m compared to that for the bedload scheme. However, the channel's plane view seemed to be stationary (Figure 9). The channel stopped wandering and started to incise immediately after the bedload removal. Then the channel continued to get deeper and narrower and the previous sand bars along the banks became ‘river terraces’.

The incision suggests that the bed structures, which formed in the bedload schemes, could not remain stable any longer. The incision depth in the upper reach was relatively large compared with that in the lower reach since the structures previously formed in the upstream reach were weaker (Table 6). Thus, the structures were strengthened especially in the upper reach. Then the structures in the upper and lower reaches became almost the same (Table 6) after the non-bedload scheme was completed. The structure variation also led to the adjustment of the corresponding channel gradient.

The non-bedload scheme in phase 3 was influenced by human interventions (Table 7). After the previous bedload scheme, artificial step-pool structures (height = 10 cm and length = 50 cm) were placed in the middle reach. Compared with phase 2, a full-scale incision was impeded (Figure 8) and only the upper reach was slightly eroded.

The results of both field investigations and experiments have indicated that, larger bed structures can protect the riverbed of channels with higher gradient by sustaining relative stability. It means that the erosive energy is dissipated by the structures and can no longer destroy the riverbed. Thus a close numerical connection must exist between the bed structures and the erosive energy they consumed.

It is obvious that the parameter S_p can directly describe the coarseness of riverbed and the structure scale to some extent. For a smooth bed without any bed structures, the value of S_p is 0. Higher S_p values represent rougher riverbeds and larger scales of structures. For a given river profile, the value of S_p is unique and operator-independent, which is a better choice than common variables such as H, L and D₅₀.

In fluvial morphology, long-term adjustment of flow and riverbed generally approaches equilibrium and stability. The balance between the structures and stream power should be satisfied when the river condition is near equilibrium and the bedload can be ignored. Thus, according to the analysis above, the development of bed structures are the results of riverbed adapting to the local hydrological regimes. If the structures are not well developed (not enough to dissipate all the energy), disequilibrium will occur and cause the riverbed to scour.

The immediate incision (Figure 8) after the transition from the bedload scheme to the non-bedload scheme in the field experiment indicates that if there is enough bedload, the riverbed can still be protected even when the existing structures cannot consume all the energy (Figure 13). In other words, a proportion of the stream power was consumed by bedload. Thus, the removal of bedload will lead to imbalance and the excessive power will erode the bed to generate new bedload. The concept that the movement of bedload will increase energy loss has also been reported elsewhere (Song & Chiew 1997; Wang & Zhang 2012; Yu et al. 2012b). Therefore, for a river section where structures and massive bedload transportation both exist, the total loss of stream power p should be expressed as the sum of these two parts.

Therefore, the form of Equation (6) is reasonable. However, due to the lack of data and the uncertainty of bedload rate measurement, Equation (7) is just a rough estimate in this study. The function f should be determined and verified carefully after further similar experiments.

In general, the total bed resistance (such as n, f_d) can be divided into two parts: the grain resistance and the form resistance (i.e. S_p in this study). In the field experiment, in the river channels where bed structures developed, the bed became so rough that the form resistance remained in domination. Therefore, S_p shows a strong influence on n and f_d in Figure 15.

Therefore, the adjustment mechanism in our field experiment can be explained by this model: (1) in the bedload scheme, g_b = g_b* so that dZ/dt = 0 (Equation (10)) and the bed was ‘protected’ by the bedload and was in equilibrium; (2) when the bedload from upstream was reduced, g_b < g_b* so that dZ/dt > 0 and the channel started to incise; (3) during incision, the bed structure intensity S_p was enhanced, which in turn resulted in the increase of roughness n (Figure 15), while the bed composition (D₉₀ and D₅₀) did not have significant change since most large boulders remained in place. I_b also increased due to the more stable bed. Thus, g_b* became smaller (Equation (11)) and the incision rate dZ/dt gradually slowed down.

Based on field work in several natural rivers and field experiments, bed structures and some of their essential principles were studied in this paper.

The evolution and distribution of structures was found to be in close relation to the hydrological conditions. The underlying principles were concluded to be: the stream power of a river section is consumed by both bed structures developed on the riverbed and bedload movement. A possible formula was derived, however further studies are still required to improve this unified energy theory, which could be an important mechanism in the research of mobile riverbed and fluvial morphology.

If the bedload can be neglected, then the channel will be stable when the equilibrium between the bed structures and stream power is reached. This means that the structures can dissipate all the erosive energy and protect the bed at this moment. A parameter called the structure intensity was defined and proven to quantify this relation well. When the structure intensity is not large enough, disequilibrium occurs and the excessive power will erode the riverbed. Generally, the river will re-adjust and new equilibrium will be reached. Therefore, the evolution of bed structures is in fact a process of the riverbed adapting to the local hydrological regimes. The fluvial morphology of streams with very coarse-grained riverbed is controlled by the dynamic process explained above.

This work was financially supported by the National Basic Research 973 Program of China (Grant No. 2012CB417002), the National Natural Science Foundation of China (Grant No. 51520105014, 51379127) and the Research Fund of Nanjing Hydraulic Research Institute (Grant No. Y215021, Y216006, Y214008).