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

  • Hamed Reza Zarif Sanayei
  • Hamed JavdanianEmail author


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.


Dam Seepage Analytical approach Nonsymmetric boundary condition Partial differential equation 



This work has been financially supported by the research deputy of Shahrekord University under grant numbers 97GRN1M1830 and 97GRN1M39422. This support is gratefully acknowledged.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringShahrekord UniversityShahrekordIran

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