PSI - Issue 84

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

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Fig. 4. F D asa function of (a)  H and (b) h bw . F L – B as a function of (c)  H and (d) h bw .

Figs. 5a-c presents the comparisons between normalized backwater-levels, head losses and water level drop ( h bw / h 0 vs h L / h 0 ,  H / h 0 vs h L / h 0 , h bw / h 0 vs  H / h 0 ) for Db01–Db03. Specifically, we found that h bw / h 0 and  H / h 0 increase monotonically with h L / h 0 (Figs. 5a-b). These results agree with the findings of Follett et al. (2020), who found that the upstream and downstream water levels adjust in response to debris‐induced flow resistance. The authors noted that  H generates a net hydrostatic pressure force that balances the drag induced by the debris obstruction. In addition, they stated that, for a given discharge and debris configuration, the upstream water depth adjusts toward a minimum‐ energy condition, resulting in a unique water level and corresponding backwater rise ( h bw ) in the upstream channel. Finally, the water depth immediately downstream of the debris ( h d,nd ) remains greater than or equal to the far‐ downstream depth ( h d ), with cases of h d,nd > h d indicating falling water at the downstream face. Under the combined action of these constraints, the water level response can be interpreted as a consequence of the redistribution of energy losses induced by the debris. Furthermore, Fig. 5c shows that the average value of h bw / h 0  0.4−0.6 (  H / h 0 ), indicating that the local head drop across the debris exceeds the net upstream backwater rise. Fig. 5d also compares the experimentally observed values of h bw / h 0 with predictions obtained from the following selected equations valid for flow obstructions. Specifically: - for trash racks and floating barriers with racks (Zayed and Saleh 2025): ℎ ℎ 0 = 6.3 ( 0 ) 2.1 ( ) 0.42 (3) - for woody debris at a debris rack (Schmocker and Hager 2013): ℎ ℎ 0 = 0.4 + 1.9 0 (4) - for a fully submerged bridge (Picek 2007):