Evaluation of seepage under hydraulic structures using gene expression programming

Abstract

The problem of seepage under concrete dams was studied numerically using finite difference code in MATLAB, after verification with GeoStudio (2018 R2) to determine the lift force under the dams, the head at the third floor of each of the dams, and the exit gradients, which all affect the functionality of these dams. The main goal of this study was to investigate the effects of cutoff locations and depths on the exit gradient and uplift pressure. An empirical equation was thus developed to predict the exit gradient by employing gene expression programming (GEP) and non-linear regression using IBM SPSS based on parameters obtained from the finite difference code. Multiple (327) runs were executed in the finite difference code for a set difference between head upstream and downstream (H=10 m) withvarious cutoffs depth (d/b), with kx/ky = 1 representing isotropic soil. For each d/b value, various cutoffs locations (x/b) were also used, with results indicating that the minimum exit gradient is observed when the cutoff location ratio at the downstream is x1/b=1 with a maximum relative depth of d1/b=0.6, while the minimum uplift pressure is observed when the cutoff location ratio at the upstream is x1/B=0, with a minimum relative depth of d1/B=0.1. The results further indicate that the maximum exit gradient is observed when the ratio of the length of upstream cutoff to the length of downstream cutoff is d1/d2 = 1. This exit gradient decrease as the ratio of d1/d2 increases. Additionally, the exit gradient decreases with increases in cutoff location and depth, while increasing with uplift pressure. Based on the simulation results, the equation obtained using the genetic expression programming model performed better in terms of predicting the exit gradient than the SPSS model, with a coefficient of determination R2 of 0.892 for training and 0.90 for testing. An empirical equation was thus derived to predict the exit gradient based on cutoff 1depth, cutoff1location, cutoff2depth and cutoff2location.