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

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Abstract

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.

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The relationships used and the description of the particle swarm optimization (PSO) algorithm is presented in the manuscript.

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  1. Department of Civil Engineering, University of Zanjan, Zanjan, Iran

    Hadi Norouzi, Jalal Bazargan, Siamak Taheri & Ahmadreza Karimipour

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  1. Hadi Norouzi
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  2. Jalal Bazargan
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  4. Ahmadreza Karimipour
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Contributions

All authors have contributed to various sections of the manuscript. All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [HN], [JB], [ST] and [AK]. The first draft of the manuscript was written by [HN] and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Hadi Norouzi.

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Norouzi, H., Bazargan, J., Taheri, S. et al. Investigation of unsteady non-Darcy flow through rockfill material using Saint–Venant equations and particle swarm optimization (PSO) algorithm. Stoch Environ Res Risk Assess 37, 3657–3673 (2023). https://doi.org/10.1007/s00477-023-02469-2

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