Regularity of transportation for cohesive bank-collapsed 1 materials 2

The transportation of bank-collapsed materials is a key issue among river 10 evolution processes. In this study, a series of flume experiments were conducted to 11 monitor riverbank collapse processes and to explore the regularity of transportation for 12 cohesive collapsed materials. The collapsed materials, both the bed and suspended 13 loads, that transformed from collapsed materials were intensively evaluated under 14 experimental conditions. The results showed that the collapsed materials contributed to 15 12~20% sedimentation in situ, 8~14% suspended loads and 70~80% bed loads. In 16 addition, the bed load motion efficiency coefficient (eb), suspended load motion 17 efficiency coefficient (es) and sediment carrying capacity factor (U /gRω) were 18 introduced to describe the transportation of collapsed materials in terms of energy 19 dissipation. This research provides theoretical and practical benefits for predicting 20 channel evolution processes. 21


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Riverbank collapse, which occurs in alluvial streams worldwide, has caused a 24 series of social, economic and environmental problems (Simon et al., 2009, Rinaldi and 25 Nardi, 2013, Hackney et al., 2015). Moreover, collapsed materials are also a major 26 stream sediment source, directly influencing sediment concentration and riverbed 27 evolution processes in both local and downstream areas (Motta et al., 2014). Thus, more 28 research has concentrated on the mechanisms and channel evolution processes 29 associated with riverbank collapse in recent years (Patsinghasanee et

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Before each experiment, the particle size distribution ( Figure 4) and physical 118 properties of experimental materials taken from typical sections were tested. At the 119 preparatory stage, the tailgate was kept closed, and the water level rose slowly to the 120 designed level. Then, the initiation of experiment began by adjusting the designed flow  After collapsed materials entered the channel, the incipient sediments were then 135 further activated and transported as bed and suspended loads, while the remaining 136 sediments accumulated at the toe of the bank. In summary, collapsed materials will be 137 transported in three patterns: accumulated sand, bed loads and suspended loads. 138 (1) Quantity of collapsed materials 139 The amount of collapsed materials was obtained by comparing the topography of 140 the riverbank before and after the experiment. Ten sections (C1, C2,…, C10) among 141 riverbanks with 20 cm intervals along the flow direction were selected to measure the 142 riverbank shape by using a glass plate with gridlines ( Figure 5). Figure 8 shows the 143 collapsed areas of the selected sections with a riverbank slope of 45°. Based on the unit 144 weight of materials listed in Table 2, the quantities of the collapsed materials can be 145 obtained in Table 3. 146   (2) Quantity of collapsed sediments accumulated at the toe of the bank 153 It is generally believed that the collapsed materials entering the channel can be 154 treated as single-particle sediments, and the incipient motion particle size was 155 calculated by the following equation ( where Ha is the atmospheric pressure expressed in terms of water column height, Ha = 158 10 m; δ0 is the thickness of a water molecule, δ0 = 3.0 × 10 −8 cm; γs is the unit weight 159 of sediment, γs = 17542 Nm -3 ; γ is the unit weight of water, γ = 9800 Nm -3 ; g is the 160 gravitational acceleration, g = 9.8 ms -2 ; D is the sediment particle size, m; Ui is the velocity for incipient sediment motion, ms -1 ; U is the velocity, ms -1 (for this study Ui = 162 U), and h is the water depth, m. 163 Table 4 presents the percentage of accumulated sediments under different 164 experimental conditions. It should be noted that particles between the lower and upper 165 limits of incipient motion particle size could be incipient, whereas others were regarded 166 as the accumulated sediments. 167 (3) Quantity of bed and suspended loads transformed from collapsed materials 169 In sediment-laden flow, coarse particles are usually transported as bed loads, while 171 fine particles are transported as suspended loads. Although there were mutual 172 transformations between these two in the transport processes, the quantities of bed and 173 suspended loads transported by the water flow remained roughly the same under certain 174 flow conditions. Thus, a critical particle size was introduced to divide the bed and 175 suspended loads, with particles larger than the critical particle size were arranged as detail in the literature (Shu et al., 2019) was adopted to obtain the critical particle size, 178 as shown in Table 5. 179 Based on the bank material particle size distribution in Figure 4, the percentage of 180 bed and suspended loads for each group can be obtained (Table 6). 181

The transportation of collapsed materials in terms of energy dissipation 183
In this study, the bed load motion efficiency coefficient (eb) and suspended load 184 motion efficiency coefficient (es) were applied to describe the transportation of collapsed 185 materials. Based on previous studies, eb represents the transformation efficiency from 186 the water potential energy into bedload motion (Bagnold, 1966) where S* is the sediment carrying capacity, m 3 s -1 ; k and m are parameters; U is the 192 velocity, ms -1 ; g is the gravitational acceleration, ms -2 ; R is the hydraulic radius, m; and 193 ω is the sediment settling velocity, m/s. The sediment carrying capacity factor (U 3 g -1 R -194 1 ω -1 ) can be regarded as the ratio of U 2 g -1 R -1 to ωU -1 , which represents the turbulence 195 intensity and action of effective gravity, respectively. For these three parameters 196 containing all kinds of energy factors, it is reasonable to study the transportation of the 197 collapsed materials by building the relationship between eb and U 3 g -1 R -1 ω -1 and between 198 es and U 3 g -1 R -1 ω -1 . The experimental data used were collected at two-minute intervals 199 in Section S3 after riverbank collapse occurred.

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The range of es is 0.0129～0.0235, which was slightly different from Bagnold's 244 result of 0.023～0.046 (Bagnold, 1966), but the values were still in the range of 245 0.00004-0.20 presented by Qian & Wan (1965). For each curve, es had a noticeably 246 negative correlation relationship with U 3 g -1 R -1 ω -1 . After the riverbank collapsed, the 247 river would transfer from a nonequilibrium state to equilibrium, and the suspended load 248 concentration would increase compared with that of the noncollapse. However, 249 sediment suspension energy decreased because of the drag reduction of suspended 250 sediments provided by Zhang (1963). Moreover, in each group, es of the lower flow 251 charge is larger than that of the higher flow, as when the flow charge increased, more 252 bed loads would transform into suspended loads, with the drag reduction of suspended 253 sediments (es decreased). 254

Discussion 255
In this study, riverbanks were built on both sides of the water flume, which was 256 different from previous correlated studies (Yu et al., 2013;Shu et al., 2019;Zhao et al., 257 2020). The similar channel shape and on-site materials made this study more scientific 258 for monitoring riverbank collapse processes. The quantities of the collapsed materials, 259 bed and suspended loads obtained by the critical particle size method presented a good 260 reference to predict the channel evolution process. The bed load motion efficiency 261 coefficient (eb), suspended load motion efficiency coefficient (es) and sediment carrying capacity factor (U 3 g -1 R -1 ω -1 ) were used to describe the transportation of collapsed 263 materials, which differed from previous literature. Thus, this study can be considered a 264 valuable attempt to scientifically describe the transportation of collapsed materials. 265 There are still limitations that need to be addressed within future research. (1) After the riverbank collapsed, the three main processes of the collapsed 280 materials were deposited on-site and transported as bed and suspended load. In terms 281 of the quantities, the percentages of these three were 12～20%, 70～80% and 8～14%, 282 respectively. 283 (2) In the transportation of the collapsed materials, the ranges of eb and es were 284 0.11～0.25 and 0.0129～0.0235, respectively. The drag reduction of the suspended 285 loads was verified by the relationships between eb, es and U 3 g -1 R -1 ω -1 . 286 (3) In terms of energy dissipation, the transportation of collapsed materials follows 287 the law of river transition from a nonequilibrium to an equilibrium state. After the 288 riverbank collapsed, the collapsed materials first transformed into bed loads. With the 289 increase in the sediment carrying factor (U 3 g -1 R -1 ω -1 ) toward the river equilibrium state, 290 more bed load sediment transformed into suspended loads. At the same time, part of 291 the energy for bed load motion would convert into the particles' potential energy. 292 The results can help reveal the mechanisms of channel bend evolution and provide 293 valuable theoretical and practical benefits to river channel embankments.

Data availability 295
All raw data can be provided by the corresponding authors upon request. 296

Author contributions 297
GD performed the measurements and wrote the manuscript draft; HL reviewed 298 and edited the manuscript. 299

Competing interests 300
The authors declare that they have no conflict of interest.