Calculation of Hydraulic Gradient within Horizontal Heterogeneous Drainage Materials Using Particle Swarm Optimization (PSO) Algorithm

The analysis of steady-state flow within rockfill materials is performed using two methods of gradually varied flow theory that analyzes the flow as one-dimensional and the Parkin equation that analyzes the flow as two-dimensional. The calculation of the hydraulic gradient (i) is of great importance in both methods. Most of the research in this area has been done in homogeneous rockfill materials and limited studies have been carried out on the flow in heterogeneous rockfill materials. In this study, we used the results of experiments in homogeneous and horizontal heterogeneous rockfill materials with three layers of aggregates with large, medium and small size. In the experimental data used in the present study, changes in hydraulic gradient relative to the flow velocity in each of the three homogeneous layers were available separately and also the changes in the horizontal heterogeneous media consisting of three layers were available separately. Due to the fact that in order to form a horizontal heterogeneous rockfill media, large, medium, and small homogeneous layers are placed on top of each other, respectively, in the approach presented in the present study, the data of the steady flow of homogeneous media are placed in the same order in the Particle Swarm Optimization (PSO) algorithm to optimize the coefficients of the binomial equation (a, b) and consequently the calculation of hydraulic gradient. In other words, in the present study, the values of the coefficients a, b, equivalent to the horizontal heterogeneous media, depending on how the homogeneous layers are placed on top of each other and only using the data of steady flow in the homogeneous media (large, medium and small size) Optimized. The results show that the difference of mean relative error (MRE) the approach presented in the present study than conditions where flow data in a horizontal heterogeneous media are directly used to calculate the coefficients a and b and consequently the hydraulic gradient, is 1.38 percent.