Modeling Seepage in Porous Media Using an Unstructured Triangular Finite Volume Algorithm

Document Type : Research Paper


1 M. Sc. student, Department of Water Engineering, College of Agriculture and Natural Resources, Razi University.

2 Assistant Professor, Department of Water Engineering, College of Agriculture and Natural Resources, Razi University


The explorers consider the study of water flow in saturated and unsaturated soils to determine the seepage, pore pressure, uplift force, and hydraulic gradient in the design of dams. Numerical simulation is a rapid low-cost method for the study of soil water flow, which has recently been increased. Many investigators have described approximate methods, based on Dupuit assumptions, to locate the surface of seepage and seepage discharge for different tailwater positions. In order to reduce the seepage discharge and, consequently, flow energy reduction passing the dam, various actions such as the construction of clay core, trench and grout certain, and clay cover on the reservoir floor have been considered. Despite all the measures taken to prevent the movement of water in the embankment dam, water always penetrates the downstream parts due to the permeability of the materials. Drainage systems are designed to collect and direct seepage of water to downstream areas, keeping the dam’s riffle slope dry to decrease the hydroscopic pressure and increase the stability of the embankment dams. Horizontal drains are widely used in homogeneous embankment dams with an average height. In this study, Richards equation was desecrated in two-dimensional and unsteady conditions using an unstructured triangular finite volume algorithm and a computer model developed to simulate seepage in saturated-unsaturated soils. In this model, Van Genuchten equation or other functions can be used to calculate hydraulic conductivity in unsaturated soil for the simulation of flow.


Main Subjects

1-    Ahmadi, H., Rezaei, H. and Zeinalzadeh, K., 2014. A Laboratory Study of the Effect of the Function of Hydraulic Conductance on Modeling of Seepage from Earth Dams. Iranian Journal of Soil and Water Research. 45(3), pp.299-307. (In Persian).
 2-    Azar, E., Sedghi-Asl, M. and Parvizi, M., 2016. Numerical Modeling of Seepage Flow Behavior from Permeable Alluvial Foundations. Journal of Applied Research in Irrigation and Drainage Structures Engineering. 16(65), pp.85-100. (In Persian).
 3-    Azizi pour, M. and Shooshtari, M., 2012. Numerical Solution of Richards's Equation in Unsaturated Flow using Finite Volume Method. Journal of Irrigation Sciences and Engineering. 35(2), pp.65-72. (In Persian).
 4-    Chakib, A. and Nachaoui, A., 2005. Nonlinear programming approach for a transient free boundary flow problem. Journal of Applied Mathematics and Computation,160 (2), pp.317-328.
 5-    Chen, J.T., Hong, H. K. and Chyuan, S.W., 1994. Boundary element analysis and design in seepage problems using dual integral formulation. Journal of Finite Element in Analysis and Design, 17 (1), pp.1-20.
 6-    Feng, F.J. and Sheng, J., 2009. A study on unsteady seepage flow through dam. Journal of Hydrodynamics, 21 (4), pp.499-504.
 7-    Ghobadian, R., 2014. Numerical simulation of saturated-unsaturated 2D- unsteady flow toward drain using finite volume method. Journal of Water and Soil. 28(3), pp.546-555. (In Persian).
 8-    Ghobadian, R. and Khodaei, K., 2009. Effects of Cutoff Wall and Drain on Uplift Pressure and Exit Gradient under Hydraulic Structure by Numerical Solution of General Equation of Fluid Flow in Soil Using Finite Volume Method. Journal of Water and Soil. 23(4), pp.148-160. (In Persian).
 9-    Hyunuk A. and Soonyoung, Y., 2014. Finite volume integrated surface-subsurface flow modeling on nonorthogonal grids. Water Resources Research, 50 (3), pp.2312-2328.
 10- Mualem, Y., 1976. A catalogue of the hydraulic properties of unsaturated soils. Research Project Report, No. 442, Technion, Israel Institute of Technology.
 11- Nabavianpour, M., 2008, Determination of the exact location of free surface leakage using boundary methods. In 4th National Congress on Civil Engineering. Tehran. Iran. (In Persian).
 12- Patankar, S. V., 1980. Numerical heat transfer and fluid flow. Hemisphere Corporation, USA.
 13- Richards, L. A., 1931. Capillary conduction of liquids through porous mediums. Physics, 1, pp.318-333.
 14- Rushton, K.R. and Youngs, E.G., 2010. Drainage of recharge to symmetrically located downstream boundaries with special reference to seepage faces. Journal of Hydrology, 380 (1), pp.94-103.
 15- Sarmah, R. and Barua, G., 2017. Analysis of three-dimensional transient seepage into ditch drains from a ponded field. Sadhana, 42 (5), pp.769-793.
 16- Shokri, N., Namin, M. and Farhoudi, J., 2017. A New Approach to Compute Water Level in Non- hydrostatic Models with Application Capabilities for Open and Porous Media Flows. Journal of Hydraulics. 11(2), pp.1-16. (In Persian).
 17- Van Genuchten, M. T., 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science of America Journal. 44(5), pp.892-898.
 18- Varjavand, P., Poreskandar, S., Parsadizadeh, D. and Masoomi, A., 2008. Physical and numerical simulation of cut-off  effect on seepage through layering foundation. Iranian water research journal. 8(14), pp.65-77. (In Persian).
 19- Yazdi, S. R. and Bayat, B., 2009. Investigating the Accuracy of Common Relationships for Calculating Homogeneous Pressure Pressure and Equivalent Weight Dams using NASIR model. Journal of Civil and Enviromental Engineering. 59(3), pp.71-82.
 20- Yousefi, M., Sedghi Asl, M. and Parvizi, M., 2015. Laboratory Study of Vertical and Inclined Sheet Pile Effects on Seepage Control and Sand Boiling Phenomenon through Alluvial Foundation of Hydraulic Structures. Iranian Journal of Soil and Water Research. 46(1), pp.59-70. (In Persian).
Volume 42, Issue 2
June 2019
Pages 89-103
  • Receive Date: 30 December 2016
  • Revise Date: 20 September 2017
  • Accept Date: 25 September 2017
  • Publish Date: 22 June 2019