## 3 Bed-Load Sediment Transport under Uniform Sand Conditions
### Effect of Unsteady Flow Characteristics on Sediment Transport Rate  
Figure 6 presents the variation of sediment transport rate with different velocity skewness under steady flow through area integration and unsteady flow conditions. The sediment transport rate under unsteady flow was significantly greater than those obtained by integrating the steady flow during the same time. In the cases of particle diameters \(d\) = 0.296 mm and \(d\) = 0.664 mm, the steady flow obtained by the integration reached the sediment incipient threshold, while in the case of \(d\) = 1.333, 2.639, and 3.741 mm, the steady flow velocity was not adequate to initiate sediment transport, and the sediment transport rate was zero. Therefore, the sediment transport result of the steady flow obtained by the  
Figure 4: Variation of sediment transport rate of five uniform sands with different velocity skewness under unsteady flow conditions.  
Figure 5: Variation of sediment transport rate of five uniform sands with different sediment particle sizes under unsteady flow conditions.  
area integration of the unsteady flow was not equivalent to that of the unsteady flow. The results indicated that the aforementioned two situations were not identical in terms of the sediment transport effect, and the unsteady flow characteristics of the flow had a great influence on the sediment transport.  
Figure 7 illustrates a comparison of the flow obtained by the unsteady flow at the same sediment transport rate and steady flow through integration. Herein, \(\Delta u\) denotes the difference between the steady flow velocity with the same sediment transport rate under unsteady flow condition and the steady flow velocity obtained by integrating the unsteady flow. It can be found that the flow rate of the steady flow was significantly greater than the steady flow rate obtained from the integration of the unsteady flow if we intend to get the same sediment transport rate. The unsteady flow had a larger impact on the sediment entrainment and souring on the riverbed.  
Figure 6: Comparison between steady flow through integration and unsteady flow transport rate under five uniform sand conditions.  
Figure 7: Velocity comparison between steady flow corresponding to the same transport rate as the unsteady flow and steady flow through integration.  
The sediment transport intensity is an effective factor to characterize the state of the bed-load movement. Combined with the experimental continuity, it is proposed to use the bed-load transport intensity dimensionless parameter \(\Phi_{1}=\frac{g_{b}}{\gamma_{s}}\Big{(}\frac{\gamma}{\gamma_{s}-\gamma}\Big{)}^{ 1/2}\Big{(}\frac{1}{gD^{3}}\Big{)}^{1/2},\Phi_{2}=\frac{g_{b}}{\gamma_{s}L,d}\) and \(\Phi_{3}=\frac{g_{b}}{\rho L,^{3}}\) to explore the relationship between the unsteadiness and sediment transport intensity [39; 40; 41].  
Taking the size distribution of uniform sand bed with \(d=0.296\)mm as an example, the relationship between the unsteady parameter \(W\) and the sediment transport intensity \(\Phi_{1}\), \(\Phi_{2}\), and \(\Phi_{3}\) was plotted. Figure 8 depicts the intrinsic law of the influence of unsteady parameters on sediment transport intensity. It was indicated that the sediment transport intensity increased with the increase of unsteady parameters (dashed line). The unsteady parameter had an exponential relationship with the sediment transport intensity. The growth rate of sediment transport intensity declined with the increase of unsteady parameters. Therefore, the relationship between the sediment transport intensity and the unsteady parameter was not simply linear, it follows \(\Phi\sim(aW^{2}+bW+c)\), where a, b, and c were constant.