Evaluation of Classical Sediment Load Formulas and Proposal of CFD-Based Deposition Formula for Deep Stormwater Drainage Tunnels

Deep stormwater drainage tunnels are increasingly being used to mitigate urban flooding, but in-tunnel sediment deposition reduces their discharge capacity and complicates their maintenance. With direct field observation constrained, numerical simulation is essential, and river-based total sediment load formulas require reassessment for use in deep tunnels. The three-phase (air–water–sediment) CFD solver SedInterFoam is first validated against a benchmark open-channel suspended sediment experiment, and is then applied to a horseshoe tunnel under a fixed design discharge for multiple inlet sediment concentrations spanning urban stormwater conditions. Four classical formulas (Yang, Shen–Hung, Ackers–White, Engelund–Hansen) are evaluated at the CFD-resolved hydraulic state; Toffaleti is omitted because its zone-based formulation is incompatible with the partially filled horseshoe geometry. The CFD consistently shows persistent retention of a substantial fraction of the inlet sediment load, whereas the transport capacity-limited interpretation of the classical formulas predicts near-complete sediment throughput—indicating structural inadequacy for the dilute, supply-limited regime typical of urban stormwater. A Universal Soil Loss Equation (USLE)-style dimensionless deposition formula is therefore proposed, with inlet sediment loading as the explicit independent variable and a tunnel correction factor 𝐾tunnel absorbing the geometric, hydraulic, and sediment variations. Its regression yields an almost linear scaling and a nearly constant deposition ratio, while analysis of the internal flow and concentration fields shows that the retained sediment is strongly concentrated near the bed and that near-bed turbulent mixing weakens moderately with a rising inlet concentration. While calibrated for a single non-cohesive settleable sand fraction, the framework provides a transferable basis for inlet-loading-dependent deposition prediction in deep stormwater drainage tunnels, and subsequent extension of 𝐾tunnel to broader sediment conditions with field-based validation is expected to enable maintenance planning, dredging volume estimation, and sediment retention risk assessment.