Hydraulic Regime Transitions at Shaft Discontinuities in Gently Sloped Tunnels

Hydraulic regime transitions and localized backwater responses can develop in gently sloped tunnels when shafts and short expansion–contraction transitions act as localized hydraulic controls. This study investigates a tunnel–shaft system using a combined theoretical, numerical, and experimental framework. A momentum-based spreadsheet model was first used to identify the discharge range at which backwater development and unsteady behavior begin. The analysis was then extended with EPA–SWMM to represent system-scale unsteady behavior and with a finite element model to resolve local hydraulic gradients near the transition. Numerical results were compared with observations from a Froude-scaled physical model. All approaches consistently showed that backwater develops primarily upstream of the shaft and that the most critical hydraulic zone is concentrated at the geometric discontinuity. A regulated entrance geometry was then evaluated as a mitigation measure. For the case analyzed, entrance regulation reduced inlet depth from 6.12 m to 3.50 m and relative filling from y/D = 0.87 to y/D = 0.503, shifting operation toward a lower-depth operating state with greater freeboard and reduced susceptibility to pressurization. The results demonstrate that shaft transitions should be explicitly considered in tunnel design and that entrance regulation can materially improve hydraulic performance.