Assessment of steady-state seepage through dams with nonsymmetric boundary conditions: analytical approach.

In this study, new analytical solutions were developed for 2D and 3D steady-state water seepage through dams with nonsymmetric boundary conditions. The nonsymmetric boundary conditions for the 2D cases were created with different unit step functions on a part and/or parts of the right boundary of dam plane. Six cases were investigated in 2D, where a constant hydraulic head is applied at the left boundary of the dam plane and rectangular, ramp, triangular, trapezoidal, tunnel, and piecewise rectangular distributions of hydraulic head are applied at the right boundary of the dam plane. Then, a 3D case with a constant hydraulic head at the upstream and a linearly distributed hydraulic head at the downstream of the dam was investigated. Subsequently, the performance of proposed analytical solutions was examined by comparison with numerical finite difference modeling. The results demonstrate reasonable accuracy of the developed equations. The developed analytical solutions can be utilized as a benchmark to verify numerical models with similar boundary conditions.

Assessment of confined aquifer response to recharge variations and water inflow distributions using analytical approach.

Quantification of the amount of the exchanged water between the surface water and a confined aquifer is a basic step in water balance and environmental hydraulics. The hydraulic connection between a surface water and a confined aquifer may occur through different recharge variations. The current research presents new analytical solutions for confined aquifer response to recharge variations and different inflow distributions. Different cases were studied, where a constant piezometric head is applied at the right boundary of the 2D confined aquifer plane and various distributions of water inflow through the recharging windows are considered on a part and/or parts of the left boundary. Finally, a uniform water inflow distribution on parts of the left boundary and a uniform distribution of water outflow at the right boundary was considered. Both steady and unsteady state problems can be solved using proposed equations. The performance of developed analytical solutions was examined compared to the numerical finite difference modeling. The results show reasonable precision of the developed analytical solutions. The developed solutions can be used as a benchmark to verify numerical approaches with similar boundary conditions.