Estimating output flow depth from Rockfill Porous media

To analyze the flow in a rockfill porous media using the Gradually Varied Flows theory (one-dimensional flow analysis) and solving the Parkin equation (two-dimensional flow analysis), calculation of the output flow depth as the downstream boundary condition is of great importance. In most previous studies, the output flow depth has been considered equal to the critical depth. In the rockfill porous media, unlike free surface channels, the fluid weight is exerted to the aggregates in addition to the flow, and therefore, the output flow depth from the rockfill is always greater than the critical depth (flow leaves the rockfill with a specific energy greater than the critical energy), and is expressed as a coefficient (Γ) of the critical depth. In the present study, using dimensional analysis and particle swarm optimization (PSO) algorithm and experimental data in different conditions (a total of 178 experimental data for rounded, crashed, Glass artificial materials with rhomboid structure, Glass artificial materials with cubic structure, sandy natural materials), an equation was presented to calculate the mentioned coefficient as a function of the physical characteristics of the rockfill porous media as well as the flow that can be used for all experimental conditions with high accuracy. If the output flow depth is considered to be equal to the critical depth, the mean relative error (MRE) in terms of using the experimental data of the mentioned materials separately and for the data of all the mentioned materials together was equal to 84.40, 83.81, 60.62, 67.68, 74.82 and 69.96%, respectively. In the case of using the proposed equation in the present study, the corresponding values of 5.49, 4.72, 6.24, 4.41, 6.42 and 8.99% were calculated, respectively.