A review of wave celerity in frictionless and axisymmetrical steel-lined pressure tunnels

Generally applicable approaches for estimating the “quasi-static”, which means without fluid–structure interaction and frequency-dependent water-hammer wave speed in steel-lined pressure tunnels are analyzed. The external constraints and assumptions of these approaches are discussed in detail. The reformulated formulas are then compared to commonly used expressions. Some special cases of wave speed calculation such as unlined pressure tunnels and open-air penstocks are investigated. The quasi-static wave speed is significantly influenced by the state of the backfill concrete and the near-field rock zone (cracked or uncracked). In the case when these two layers are cracked, the quasi-static wave speed is overestimated in between 1% and 8% compared to uncracked concrete and near-field rock layers. Depending on the stiffness of steel liner and penstock, the fluid–structure interaction leads to significant difference in wave speeds values. Compared to the quasi-static case, the fluid–structure interaction approach, applied to steel-lined tunnels, results up to 13% higher wave speed values in the high-frequency range (higher than 600 Hz) and up to 150% lower values for frequencies between 150 and 300 Hz in the considered test case.