# Numerical Study of the Flow and Blockage Ratio of Cylindrical Pier Local Scour
## 1 Introduction  
Scour erosion refers to an increase in local sediment transport at the base of a submerged structure due to the vortices generated by fluid-structure interactions. According to [PERSON] and [PERSON] (1983)[1], scour in rivers can be classified into three categories:  
1. General scour, which occurs irrespective of the presence of an obstacle. 2. Contraction scour, which occurs as a result of constriction due to lateral groins, spur dikes, or bridge abutments. 3. Local scour, which is only observed at the base of the obstacle and does not lead to sediment transport far from the pier. [PERSON] and [PERSON] (1983)[1], distinguish the first and last types as live-bed scour and clear-water scour, respectively. The shear stress exerted by the approaching flow determines the type of scour at the base of a structure. Clear-water scour occurs as a result of inflow shear stresses which are less than or equal to the threshold for sediment motion, whereas live-bed scour occurs for inflow shear stresses that are greater than this threshold ([PERSON] et al., 1999[2]). In the literature, this threshold between clear-water and live-bed conditions has been described in a number of ways. [PERSON] et al. (2017[3]), expressed it as the meanvelocity needed for the entrainment of the bed, while [PERSON] et al., 2005 [4], expressed it as a critical value for the Shields number associated with the friction velocity, \(u_{\tau}\). Examples of clear-water conditions can be found in nature, such as at the Tahrir and Imbaba bridges in Cairo, Egypt ([PERSON] et al., 1991 [5]), and also in laboratory studies ([PERSON] et al., 2018 [6]). Scouring at the base of bridge piers has been found to be the third global cause of bridge collapse ([PERSON], 2018 [7]) after impact and flooding. However, the leading causes of bridge collapse vary significantly in dependence with the geographical situation, construction and inspection standards ([PERSON] et al., 2012 [8]). As a result, some regional studies have found that bridge scouring is responsible for between 50% and 64% of bridge failures [9; 10; 11; 12]. This problem highlights the importance of studying the scouring process; hence, there is interest in numerical models capable of accurately modeling this case. The characteristics of the flow around a cylindrical pier are well known, and the turbulent structures present have been extensively described in the past [4; 13; 14; 15]. Upstream from the cylinder, the main structure responsible for scouring is a horseshoe vortex (HSV) system. This is also the case downstream in live-bed conditions, but in clear-water conditions, the HSV competes against wake vortices (WV) in the deposition and scouring processes ([PERSON] et al., 2018 [16]). However, despite the many existing studies on pier scouring, our current understanding of this process remains incomplete. A recent study by [PERSON] et al., 2022 [17], pointed out that the gap between the numerical predictions of equilibrium scouring and experimental results can be traced to the limitations of the current sediment transport theory. As [PERSON], 2018 [18], observed, there is a noteworthy disparity between studies of live-bed scouring [4; 19; 20; 21; 22; 23; 24; 25] and clear-water scouring [26; 27; 28; 29], the latter being much less studied. There are many empirical and semi-empirical formulae for predicting bedload transport available in the literature ([PERSON], 1993 [30], but their predictions differ in certain regimes. Most sediment models need a sand-slide model to control the angles of scouring and deposition ([PERSON], 2019 [31]). In clear-water conditions, the majority of models consider the bed load [27; 28; 29], although the suspended load has been considered for flow velocities in the upper spectrum ([PERSON] and [PERSON], 1993 [26]. The usual approaches for turbulence modeling include RANS [26; 27] and URANS ([PERSON] et al., 2012 [28]) approaches.