PSI - Issue 84

Stefano Pagliara et al. / Procedia Structural Integrity 84 (2026) 1270–1277

1275

ℎ ℎ 0 = 7.43 ( ℎ )

1.79 ( 1 1.33 ( 1

0 .054 )( 2 2 ) ℎ 0 0 .009 )( 2 2 ) ℎ 0

(5 ) (5 )

- for a partially submerged bridge (Picek 2007): ℎ ℎ 0 = 3.22 ( ℎ ) where, y x = h uB when h * < 1; otherwise, y

x = height of obstacle. Fr 0 , Fr d and V d are initial Froude number, downstream Froude number and downstream velocity respectively. All equations hereby have been expressed using the symbols and normalization adopted in the present study. The comparison shown in Fig. 5d indicates that these equations are not suitable for the tested debris configurations as they significantly underpredict h bw , except for very low backwater conditions. This reduced performance is likely due to the limited number of governing variables included in the formulations. In addition, the debris configurations used in the present study’s experiments have complex geometries, which are not accounted for in the mentioned studies.

Fig. 5. (a) h bw / h 0 as a function of h L / h 0 ; (b)  H / h 0 as a function of h L / h 0 ; (c) h bw / h 0 as a functions of  H / h 0 ; (d) comparison of observed and predicted values of h bw / h 0 using Eqs. (3), (4) and (5).

Figure 6 shows variation of C D / C L with h u / H D for Db01–Db03. h u / H D expresses the degree of relative submergence of the debris within the upstream flow. C D / C L decreases monotonically with h u / H D , with the largest ratios observed for the impervious debris Db03. Notably, as h u / H D increases, C D / C L rapidly decreases asymptotically tending to 0. Under these conditions, the differences between debris configurations become negligible under unbounded flow conditions (Malavasi and Guadagnini 2007). These preliminary results suggest that we are still far from a complete understanding of the undelaying physics governing the hydrodynamic loads under complex debris configurations, thus paving the way for future research.