Darcy’s Law Equation with Application to Underground Seepage in Earth Dams in Calculation of the Amount of Seepage

Koros Kiplangat Vincent¹, Mutua Nicholas Muthama^1, and Sakayo Nicodemus Muoki¹

¹Mathematics and Informatics Department, Taita Taveta University College, Voi, Kenya

Cite this paper

Koros Kiplangat Vincent, Mutua Nicholas Muthama and Sakayo Nicodemus Muoki. Darcy’s Law Equation with Application to Underground Seepage in Earth Dams in Calculation of the Amount of Seepage. American Journal of Applied Mathematics and Statistics. 2014; 2(3):143-149. doi: 10.12691/AJAMS-2-3-8

Abstract

Water is a very important natural resource that no creation can exist without it. Hence it has become a responsibility of every person to try and conserve this very precious resource. One of the ways of conservation is by building earth dams. However if they are not well managed these dams may end up drying up due to underground seepage leading to failure of the dam. In this paper we are concerned with how to calculate the discharge rate through a porous medium, the velocity of the discharge and finally the total discharge using Darcy’s law. This study will also describe a computer based model that accepts input and calculate the amount of discharge per given time. From Darcy’s law it is shown that, the discharge rate depends among other factors the porosity of the medium. So from the study we were able to determine which medium is able to hold water rather than supporting percolation.

Keywords

seepage, discharge rate, Darcy’s law, porosity

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]	Bednárová, et al. (2001): Analýzafiltračnéhopohybuna VD Starina v roku 2001 (Analysis of seepage flow at the waterworkStarina). STU, Bratislava, 94 pp. (In Slovak).
[2]	Willowstick (2010): Carbon Capture and Storage Class (UU and NM (2010): Supplemental Notes about GW Flow Equation.
[3]	Darcy, Henry (1856). Les fontaines publiques de la vile de Dijon. Paris: Dalmont.
[4]	Gevorkian, G., (2004.) "Darcy's Law and Underground Water Flow," California State Science Fair Abstract [accessed October 21, 2011].
[5]	Huang T. K. (1994): “Stability analysis of an earth dam under steady state seepage.” Computers and Structures, Vol. 58, No. 6, pp 1075-1082.
[6]	Lambert, J., Veenbergen, V., Van der Hoek, E. and Karstens, S., (2004.): Environment BioSealing: How Micro-Organisms Become Our Little Allies in Repairing Leaks. Ingeokring Newsletter, Vol.11. No.1, pp. 9-12.
[7]	Kamanbedast, A.B., A. Norbakhsh and R.Aghamajidi,( 2010): Seepage Analysis of earth dams with using seep/w Software Case study: Karkhehdam. World Academy of Science, Engineering and Technology, 69: 1272-1277.
[8]	Liao Hongzhi, (2005): Experimental study on BioSealing technique for seepage prevention.MSc. thesis, UNESCO-IHE Institute for Water Education/GeoDelft, Delft, the Netherlands.
[9]	Marino, M. and Luthin, J.N., (1982).Seepage and Groundwater, (Elsevier Scientific Publishing Company, New York), pp. 107-112.
[10]	Mullen, K., (2011): "Darcy's Law," National Groundwater Association [accessed October 21, 2011].
[11]	Wikipedia contributors, (2011). "Darcy's Law," Wikipedia, The Free Encyclopedia [accessed October 21, 2011].