## 1 Introduction  
The unsteady flow caused by storm waves and other disasters in nature often causes severe sediment movement and significant morphological changes, which exhibit extremely harmful effect to human activities and buildings [1; 2]. These strong flows cause significant erosion and deposition in affected coastal areas, and results in severe economic losses [3]. The unsteady flow is characterizedas a process of acceleration or deceleration and a strong unsteadiness effects on sediment particles during a short time [4; 5; 6; 7], which affects the threshold motion of sediment and bed-load transport. Besides, sediment transported in natural coastal zone and rivers is usually heterogeneous in particle sizes. A further consequence of mixed grain sizes shows that sediment transport rate is controlled not only by water hydraulics but also by the interaction between different sized particles within transported sediment and bed materials [8]. Recent experimental studies provide some insight for better understanding mechanisms involved in sediment transport under different flow conditions. The uniform and non-uniform sediment transports under steady flow condition have been extensively studied [9; 10; 11; 12]. Besides, some numerical simulations were carried out under unsteady flow condition [13; 14; 15; 16]. The above studies were mostly focused on uniform sediment under steady flow conditions. The force acting on the sediment particle was more complicated under unsteady flow compared to steady flow [17]. In addition to the conventional forces such as drag force, the particles are also usually suffered to some additional forces caused by the sharp change of flow velocity. The representative one of those forces is defined as inertia force that is non-negligible, which could characterize additional loading on the particles under unsteady flow, and that will disappear in the steady flow [18]. Meanwhile, the unsteadiness of flow has significant effects on the structure of flow field and the sediment movement since unsteadiness enhances sediment transport [19]. Some researchers introduced unsteady parameters to characterize the unsteadiness effect on flow structure and sediment transport, and then the relationship between uniform sediment transport intensity and unsteady flow parameters has been established [20; 21]. The transport rate was closely related to the unsteady parameters of the water flow [22]. [PERSON] et al. [23] calculated the changes in shear stress during the flood process and measured the sediment transport rate for a range of hydrograph durations and shapes. It was considered that the total sediment transport capacity was slightly affected by the transient stress of the unsteady flow which had been also found in natural rivers [24; 25]. [PERSON] and co-workers stated that the initial bed conditions and unsteadiness of flow had significant effects on bed-load transport intensity and total sediment yield [26]. The unsteadiness of flow exhibits influence on bed-load transport rate through variable bed shear stress and stream power. Turbulence condition plays an essential role in the entrainment of sediment. Under turbulent flow condition, [PERSON] et al. [27] and [PERSON] et al. [28] found that in addition to the magnitude of the instantaneous turbulent forces applied on a sediment grain, the duration of these turbulent forces was also important in determining the sediment grain's threshold of motion via entrainment experiments. Although many studies have been carried out on sediment movement under unsteady flow, most of these were based on general unsteady flow that originated from open channel flows. For the unsteady flow such as floods and storm waves with strong flow unsteadiness and high sediment transport intensity, whether these theories and formulas are valid needs further investigations. Furthermore, none of the above considered the influence of sediment particle size.