Single-objective geometry optimization of cutoff walls in concrete gravity dam foundations using a surrogate-assisted FEM–ANN–SSOA framework

This study presents an integrated Finite Element Method–Artificial Neural Network–Salp Swarm Optimization Algorithm (FEM–ANN–SSOA) framework for single-objective geometry optimization of cutoff walls in concrete gravity dam foundations. A validated Finite Element Method (FEM) numerical model of the Pine Flat Dam was developed using ABAQUS software to generate a comprehensive database comprising 77 numerical simulation scenarios by systematically varying cutoff wall depths ( d ) and distances ( x ) from the upstream heel. The numerical findings revealed a strong nonlinear interaction between the geometric design parameters; specifically, increasing the cutoff wall depth from 9 to 18 m reduced the maximum foundation uplift pressure ( U_max ) by 42% when the wall was located 40 m from the upstream heel, whereas the reduction was constrained to only 29% when positioned at a distance of 140 m. To eliminate the high computational burden associated with repetitive numerical simulations during metaheuristic search, an Artificial Neural Network (ANN) surrogate model was developed and trained. The optimized ANN surrogate achieved high predictive accuracy on independent test datasets ( R²=0.9982, RMSE=0.0084\; MPa, MAE=0.0061\; MPa, and MAPE=0.72% ). Furthermore, a 5-fold cross-validation scheme confirmed its statistical robustness (mean R²=0.9965 ). Crucially, the ANN surrogate provided a substantial computational speed-up factor of approximately 60,000× compared to standalone FEM iterations. Coupling this high-fidelity surrogate model with the Salp Swarm Optimization Algorithm (SSOA) enabled efficient design space exploration, identifying the practical optimal configuration at a depth of d=21\; m and a distance of x=40\; m from the upstream heel. This optimized layout reduced the maximum foundation uplift pressure by 65.3% compared to the least favorable geometric configuration. While deeper cutoff walls moderately increased the localized exit hydraulic gradient ( iₑₓᵢₜ ), all evaluated values remained well below the critical failure threshold ( icrit=1.0 ) against piping. The proposed FEM–ANN–SSOA framework provides a reliable, high-performance decision-support tool for the rapid engineering optimization and hydro-mechanical safety assessment of concrete gravity dam foundations.