PSI - Issue 62

Michele Palermo et al. / Procedia Structural Integrity 62 (2024) 593–600 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Furthermore, tests were conducted by varying the debris percentage blockage ratio  A=100[(d d  D)t d ]/(bh) and the total cross-sectional area blocked by both pier and debris accumulation A acc =(d d  D)t d +hD. Based on dimensional arguments, Pagliara et al. (2010a) found the non-dimensional scour depth can be expressed as follows, with n s indicating the geometric surface roughness of the sill or gabion in mm and T * =hUt/A acc is the non-dimensional time: � ��� � ���∆ , � � � , ℎ � , � �� � , � � � , � � � , � � , � � � , ∗ � (1) Based on the kinetics of the scour evolution and its features, Pagliara et al. (2010a) distinguished four different phases in the presence of debris accumulation (Fig. 2): a) the scour hole only forms upstream of the pier and evolves like in the reference tests when debris is absent (i.e., Phase 1 occurring for 0 ≤ T * ≤ T * 1 and characterized by a temporal scour evolution coefficient  1 ; see Fig. 3a); b) the hole reaches the sill and its presence starts delaying the expansion of the hole and dune (Phase 2, occurring for T * 1  2 ). Furthermore, a secondary scour formation occurs downstream of the sill (Fig. 3b); c) in Phase 3 (occurring for T * 2  3 ). However, the scour hole enlarges transversally in correspondence with the sill, whereas the secondary scour formation downstream of the sill continues evolving resulting in a prominent downstream dune (Fig. 3c); finally, Phase 4 (occurring for T * 3

Fig. 2. Different phases distinguished by Pagliara et al. (2010a).

As mentioned, the analysis of all the phases was conducted in detail by Pagliara et al. (2010a), who also provided useful tools to evaluate the scour evolution at different non-dimensional times T * (see Appendix in Pagliara et al., 2010a). Very importantly, the transition between the (i-1)- to the i-phase occurs at T * i , with i indicating an integer ranging from 0 to 4 and T * 0 =0. The non-dimensional transition time T * i depends on several parameters, including the relative water depth, the non-dimensional distance of the sill, the surface roughness of the protection structure and the characteristics of the debris accumulation. Overall, experimental evidence allowed authors to establish that: a) in the absence of debris accumulation, scour features do not depend on the tested sill type, i.e., the efficiency of different tested countermeasures were comparable; b) the effectiveness of protection structures in controlling scour expansion significantly reduces in the presence of debris accumulation and depends on their geometric characteristics and (slightly) on the sill roughness; c) the efficiency of the countermeasure further reduces when the sill becomes exposed. Namely, initially the presence of the sill delays the scour evolution but, when the downward flow directly impacts on it, the kinetics of the erosion process rapidly varies, resulting in a significant increase of the scour evolution coefficient (that reflects the increase of the scour velocity). Such occurrence generally takes place for high values of  A and it is particularly