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

  • Hamed Reza Zarif Sanayei
  • Hamed JavdanianEmail author
Article
  • 21 Downloads

Abstract

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.

Keywords

Dam Seepage Analytical approach Nonsymmetric boundary condition Partial differential equation 

Notes

Acknowledgements

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

References

  1. Chen, J. T., Hong, H. K., & Chyuan, S. W. (1994). Boundary element analysis and design in seepage problems using dual integral formulation. Finite Elements in Analysis and Design, 17, 1–20.CrossRefGoogle Scholar
  2. Chesnaux, R. (2016). Closed-form analytical solutions for assessing the consequences of sea-level rise on unconfined sloping island aquifers. Global and Planetary Change, 139, 109–115.CrossRefGoogle Scholar
  3. El Tani, M., Kamali, A., & Gholami, M. A. (2019). Analytic assessment of the water table drawdown, seepage, and back pressure at Rudbar PSPP. Rock Mechanics and Rock Engineering, 52(7), 2227–2243.CrossRefGoogle Scholar
  4. Fu, J., & Jin, S. (2009). A study on unsteady seepage flow through dam. Journal of Hydrodynamics, 21, 499–504.CrossRefGoogle Scholar
  5. Fukuchi, T. (2016). Numerical analyses of steady-state seepage problems using the interpolation finite difference method. Soils and Foundations, 56, 608–626.CrossRefGoogle Scholar
  6. Fusi, L., Farina, A., & Rosso, F. (2015). Mathematical models for fluids with pressure-dependent viscosity flowing in porous media. International Journal of Engineering Science, 87, 110–118.CrossRefGoogle Scholar
  7. Javdanian, H. (2019). Predicting seismic slope displacements of embankment dams using fuzzy systems. Journal of Dam and Hydroelectric Powerplant, 5(19), 25–35.Google Scholar
  8. Javdanian, H., & Jafarian, Y. (2018). Dynamic shear stiffness and damping ratio of marine calcareous and siliceous sands. Geo-Marine Letters, 38(4), 315-322.Google Scholar
  9. Javdanian, H., & Lee, S. (2019). Evaluating unconfined compressive strength of cohesive soils stabilized with geopolymer: a computational intelligence approach. Engineering with Computers, 35(1), 191-199.Google Scholar
  10. Javdanian, H. (2019). Evaluation of soil liquefaction potential using energy approach: experimental and statistical investigation. Bulletin of Engineering Geology and the Environment, 78(3), 1697-1708.CrossRefGoogle Scholar
  11. Javdanian, H., & Pradhan, B. (2019). Assessment of earthquake-induced slope deformation of earth dams using soft computing techniques. Landslides, 16(1), 91–103.CrossRefGoogle Scholar
  12. Javdanian, H., Shakarami, L., & Zarif Sanayei, H. R. (2018a). Modeling seismic settlement of earth dams due to earthquake loading. International conference on new findings of civil, architectural and Iran building industry, 11 December, Tehran.Google Scholar
  13. Javdanian, H., Zarif Sanayei, H. R., & Shakarami, L. (2018b). A regression-based approach to predict crest settlement of embankment dams under earthquake shaking. Scientia Iranica.  https://doi.org/10.24200/sci.2018.50483.1716.CrossRefGoogle Scholar
  14. Kacimov, A., & Obnosov, Y. (2012). Analytical solutions for seepage near material boundaries in dam cores: the Davison–Kalinin problems revisited. Applied Mathematical Modelling, 36, 1286–1301.CrossRefGoogle Scholar
  15. Kacimov, A. R., & Obnosov, Y. V. (2019). Modelling of 2-D seepage from aquifer towards stream via clogged bed: the toth-trefftz legacy conjugated. Advances in Water Resources, 131, 103372.CrossRefGoogle Scholar
  16. Kazemzadeh-Parsi, M. J., & Daneshmand, F. (2013). Three dimensional smoothed fixed grid finite element method for the solution of unconfined seepage problems. Finite Elements in Analysis and Design, 64, 24–35.CrossRefGoogle Scholar
  17. Leontiev, A., & Huacasi, W. (2001). Mathematical programming approach for unconfined seepage flow problem. Engineering Analysis with Boundary Elements, 25, 49–56.CrossRefGoogle Scholar
  18. Li, M., Guo, X., Shi, J., & Zhu, Z. (2017). Seepage and stress analysis of anti-seepage structures constructed with different concrete materials in an RCC gravity dam. Water Science and Engineering, 8, 326–334.CrossRefGoogle Scholar
  19. Liang, X., & Zhang, Y. K. (2013). Analytic solutions to transient groundwater flow under and time-dependent sources in a heterogeneous aquifer bounded by fluctuating river stage. Advances in Water Resources, 58, 1–9.CrossRefGoogle Scholar
  20. Mohsenian, A. R., Sedghi-Asl, M., & Rahimi, H. (2019). An analytical solution for confined seepage problem beneath hydraulic structures. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 43(2), 361–369.CrossRefGoogle Scholar
  21. Nasiri, F., Javdanian, H., & Heidari, A. (2019). Behavior of earth dams due to downsampling-based records. In: 8th International Conference on Seismology and Earthquake Engineering (SEE8), 11 November, Tehran, Iran.Google Scholar
  22. Navas, P., Lopez-Querol, S., Yu, R. C., & Li, B. (2016). B-bar based algorithm applied to meshfree numerical schemes to solve unconfined seepage problems through porous media. International Journal for Numerical and Analytical Methods in Geomechanics, 40(6), 962–984.CrossRefGoogle Scholar
  23. Nourani, V., Aminfar, M. H., Alami, M. T., Sharghi, E., & Singh, V. P. (2014). Unsteady 2-D seepage simulation using physical analog, case of Sattarkhan embankment dam. Journal of Hydrology, 519, 177–189.CrossRefGoogle Scholar
  24. Pedroso, D. M. (2015). A solution to transient seepage in unsaturated porous media. Computer Methods in Applied Mechanics and Engineering, 285, 791–816.CrossRefGoogle Scholar
  25. Rakhshandehroo, G. R., & Pourtouiserkani, A. (2013). Predicting Doroodzan dam hydraulic behavior during rapid drawdown. Iranian Journal of Science and Technology, Transaction of Civil Engineering, 37, 301–310.Google Scholar
  26. Rezk, M. A. E. R. M., & Senoon, A. E. A. A. A. (2012). Analytical solution of earth dam with upstream blanket. Alexandria Engineering Journal, 51, 45–51.CrossRefGoogle Scholar
  27. Serrano, S. E., & Workman, S. R. (1998). Modeling transient stream/aquifer interaction with the non-linear Boussinesq equation and its analytical solution. Journal of Hydrology, 206, 245–255.CrossRefGoogle Scholar
  28. Shakarami, L., Javdanian, H., Zarif Sanayei, H. R., & Shams, G. (2019). Numerical investigation of seismically induced crest settlement of earth dams. Modeling Earth Systems and Environment, 5(4), 1231–1238.Google Scholar
  29. Tan, X., Wang, X., Khoshnevisan, S., Hou, X., & Zha, F. (2017). Seepage analysis of earth dams considering spatial variability of hydraulic parameters. Engineering Geology, 228, 260–269.CrossRefGoogle Scholar
  30. Teloglou, I. S., & Bansal, R. K. (2012). Transient solution for stream–unconfined aquifer interaction due to time varying stream head and in the presence of leakage. Journal of Hydrology, 428, 68–79.CrossRefGoogle Scholar
  31. Wei, B., Gu, M., Li, H., Xiong, W., & Xu, Z. (2018). Modeling method for predicting seepage of RCC dams considering time-varying and lag effect. Structural Control and Health Monitoring, 25(2), 1–14.CrossRefGoogle Scholar
  32. Yuan, S., & Zhong, H. (2016). Three dimensional analysis of unconfined seepage in earth dams by the weak form quadrature element method. Journal of Hydrology, 533, 403–411.CrossRefGoogle Scholar
  33. Zarif Sanayei, H. R., Talebbeydokhti, N., & Moradkhani, H. (2015). 3D estimation of metal elements in sediments of the Caspian Sea with moving least square and radial basis function interpolation methods. Scientia Iranica, Transaction A: Civil Engineering, 22(5), 1661–1673.Google Scholar
  34. Zarif Sanayei, H. R., Talebbeydokhti, N., & Rakhshandehroo, G. R. (2019). Analytical solutions for water infiltration into unsaturated–semi-saturated soils under different water content distributions on the top boundary. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 43(4), 747–760.Google Scholar
  35. Zhang, W., Dai, B., Liu, Z., & Zhou, C. (2017). Unconfined seepage analysis using moving kriging mesh-free method with Monte Carlo integration. Transport in Porous Media, 116(1), 163–180.CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringShahrekord UniversityShahrekordIran

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