Investigation of unsteady non-Darcy flow through rockfill material using Saint–Venant equations and particle swarm optimization (PSO) algorithm

• Published in: Stochastic environmental research and risk assessment Vol. 37; no. 9; pp. 3657 - 3673
• Main Authors: Norouzi, Hadi, Bazargan, Jalal, Taheri, Siamak, Karimipour, Ahmadreza
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2023; Springer Nature B.V
• Subjects: Algorithms; Aquatic Pollution; Chemistry and Earth Sciences; Coefficients; Computational Intelligence; Computer Science; Dam construction; Discharge; Earth and Environmental Science; Earth Sciences; Environment; Flood control; Flood hydrographs; Flow characteristics; Flow control; Flow velocity; Hydraulic gradient; Hydraulic structures; Hydraulics; Math. Appl. in Environmental Science; Mathematical analysis; Open channels; Original Paper; Particle swarm optimization; Physics; Probability Theory and Stochastic Processes; Rockfill dams; Sensitivity analysis; Statistics for Engineering; Unsteady flow; Waste Water Technology; Water Management; Water Pollution Control; Sensitivity analysis of dx and dt parameters; Particle swarm optimization (PSO) algorithm; Unsteady non-Darcy flow; Rockfill materials; Saint–Venant equations
• ISSN: 1436-3240; 1436-3259
• DOI: 10.1007/s00477-023-02469-2

Rockfill materials are widely used in construction of rockfill dams and flood control structures. Analysis of the unsteady flow through rockfill materials is of great importance. Calculations of water surface profile at different times, flood hydrographs (temporal changes in flow discharge) at different reaches and temporal changes of depth at different intervals through the rockfill materials are widely used in the design of the hydraulic structures. In the present study, using the experimental data and the Saint–Venant equations, the unsteady flow through the rockfill materials was studied. Since the hydraulic gradient inside the rockfill materials is equal to the slope of the energy line in open channels, considering the temporal changes of the unsteady flow discharge and depth and consequently, temporal changes in the hydraulic gradient with respect to the flow velocity, different values of the binomial equation coefficients "a" and "b" were optimized every 1 s using the Particle Swarm Optimization (PSO) algorithm and combining it with the Saint–Venant equations. In addition, the sensitivity analysis as well as the effects of spatial step (dx) and time step (dt) on calculation of the unsteady flow characteristics were also addressed. The results indicated that if instead of using the fixed values for the coefficients "a" and "b", variable values are used for the mentioned coefficients at different times, the Saint–Venant equations are more accurate in the analysis of the unsteady Non-Darcy flow.