Numerical modeling of optimal location of drainage and cutoff wall under small concrete dams

Abstract

This study presents a rigorous investigation into determining the optimal placement of a drainage well and cutoff wall to effectively mitigate the uplift force and seepage discharge in small concrete dams. A sophisticated numerical model based on the two-dimensional Laplace equation was developed for this purpose. The Laplace equation was discretized using the finite difference method with a second-order central schema, and the resulting system of equations was efficiently solved using the Gauss–Seidel method with an over-relaxation factor of 1.95. The Neumann boundary conditions were applied to the dam body and cutoff wall, while Dirichlet boundary conditions were imposed on the drainage well, as well as the upstream and downstream sections of the dam. The results exhibited an excellent agreement between the numerical simulations and the observed data, with a mean absolute percentage error of 3.54%. The findings from the numerical simulations revealed that the optimal location for the drainage well is at a distance of 0.2L from the upstream face of the dam, where L represents the dam length. This location resulted in a notable reduction of approximately 38% in the uplift force. Additionally, utilizing a cutoff wall at the upstream portion of the dam led to a reduction of about 15% in the uplift force. Remarkably, when both a cutoff wall and a drainage well were employed at their respective optimal locations, the uplift force decreased by an impressive 53%.