## 1 Introduction
The mutual interference among different components in particle size makes the calculation of bed-load initiation and transport rates more complicated [29; 30]. Generally, when dealing with the bed-load transport rate of non-uniform sediment, a kind of bed-load representative of particle sizes was proposed, and then the total bed-load transport rate of non-uniform sediment was calculated by using the transport formula of uniform sediment [31]. Otherwise, the non-uniform sediment particle size is grouped and the fractional sediment transport rate is calculated by using the formula of uniform sediment [32]. [PERSON] et al. [33] proposed a method to calculate the bed-load transport rates of two bimodal components by using two independent fractions of fine and coarse sand. The results indicated that the proportion of non-uniform sand components had a great impact on sediment transport rate. As for the insufficient effect of existing relationships on bimodal sediments, [PERSON] et al. [34] developed a new relationship for fractional bed-load transport considering the critical shear stress of non-uniform unimodal and bimodal sediments. [PERSON] et al. [35] developed a bed-load transport model for the prediction of the transport rate of non-uniform sediment that considered the density function of sediment entrainment with no active layer. Due to the non-uniformity of bed-load sediment particles, the distribution of sediment transport was affected by the interaction among particles, such as hiding and exposure effects [12; 36]. [PERSON] et al. [21] proposed formulas with a correction factor to explain the hiding and exposure mechanisms of non-uniform sediment transport. The formulas were used to calculate the fractional transport rates of non-uniform bed load and suspended load. The results obtained based on steady flow are not enough to explain the principles of non-uniform sediment transport under unsteady flow. The initiation and transport movement of non-uniform and non-cohesive sediment under unsteady flow is more complicated. The mechanisms of initiation and transport have not been explained clearly, and further research is still needed. There are few studies focusing on the non-uniform sand transport under unsteady flow due to its complexity, but it is important in improving the theory of sediment movement and guiding sand beach regulation projects. Therefore, a physical modeling non-uniform and non-cohesive sediment motion under unsteady flow condition was conducted by referring to the basis of uniform sediment movement under unsteady condition. The objective of this paper is to investigate the influence of unsteady flow on sediment incipient motion and transport, and compare bed-load transport rates with varying flow and sediment conditions. A new unsteadiness parameter based on the acceleration concept was proposed to examine the effect of unsteadiness on the mechanism of sediment transport under unsteady flow conditions. A suitable parameter to represent horizontal inertial force in the theoretical model is selected to evaluate effects of different velocity skewness on bed-load movement. This study tests the theoretical model against experimental data obtained under unsteady flow to see whether there is a good fit. Additionally, the relationship between the travel distance and velocity skewness of sediment particles is built to show a change in the trend.