Modified Schaffernak’s Solution for Seepage Through Earth Dam

Arinze Emmanuel Emeka; Agunwamba Jonah Chukwuemeka

doi:doi:10.11648/j.mma.20180304.11

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Modified Schaffernak’s Solution for Seepage Through Earth Dam

Arinze Emmanuel Emeka, Agunwamba Jonah Chukwuemeka

Published in Mathematical Modelling and Applications (Volume 3, Issue 4)

Received: 6 November 2018 Accepted: 6 December 2018 Published: 3 January 2019

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Abstract

Seepage analysis forms an important and basic part of geotechnical engineering owing to its importance in ground water contamination control, slope stability analysis and dam design. Furthermore, It is important for determining the distribution of seepage uplift pressures and the resulting seepage forces as well as the estimation of the volume of seepage losses through the body and the foundation of earth dams. Casagrande (1940) and Schaffernak (1916) improved on Dupuit’s solution of seepage through earth dam without considering tail water. In this work, modification of Schaffernak’s model was done to accommodate tail water. Values obtained using the new model though similar to that of the three other models (Dupuit, Casagrande and Schaffernak) shows that existence of tail water affects the value of seepage. The new model is very consistent from 3-6 m height. Though the seepage equation from the new model is similar to that of Casagrande, they differ because the value of seepage face for the tail water ‘a’, used for computations are not the same. For each of the model, there is a linear relationship between the seepage and the height of water upsream. Interestingly, there is a sharp change in seepage at 6m height of dam with increase in slope between 6 m and 9 m for each model except at the slope of 1:2.5 where a decrease in slope was recorded for the new model.

Published in	Mathematical Modelling and Applications (Volume 3, Issue 4)
DOI	10.11648/j.mma.20180304.11
Page(s)	44-50
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Seepage, Calculus, Earth Dam, Scaffernak’s Solution, New Seepage Equation

References

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[2]	Mishra, G. C. and Singh, A. K. (2005) Seepage through a Levee. International Journal of Geomechanics 5(1):31-40.
[3]	Zhang, L. M., Xu, J. and Jra, J. S. (2009) Analysis of earth dam failure: A database approach Journal of Georisk 3(3):184-189.
[4]	Taypur, G., Swiatek, D., Wifa, A. and Singh, V. P. (2005) Case study: finite element method and artificial neural network models for flow through Jeziorsko earthfill Dam in Poland. Journal of Hydraulic Engineering 731(6):1-8.
[5]	Thieu, N. T. M., Fredlund, M. D., Fredlund, D. G and Hung, V. Q. (2001) Seepage modeling in a saturated/unsaturated soil system. International Conference on Management of the Land and Water resources.
[6]	Giglou, A. N. and Zerratparvar, A. (2012) Seepage estimation through earth dam. Journal of Basic and Applied Scientific research, 2012;1(1):1-5.
[7]	Gui, S., Zhang, R., Turner, J. P and Xue, X. (2000). Probabilistic slope stability analysis with stochastic hydraulic conductivity. Journal of Geotechnical and Geoenvironmental Engineering 126(1):41-47.
[8]	Srivastava, A., Badu, G. L. S. and Haldar, S. (2010) Influence of spatial variability of permeability property on steady state seepage flow and slope stability analysis. Dams 11(3-4):93-101.
[9]	Budhu, M. (2011) Soil mechanics and Foundation, John Wiley & sons, New Jersey.
[10]	Kokaneli, S. P., Maghsoodian, S. Molaabasi, H. and Kordnaeij, A. (2013) Seepage evaluation of earth dam using Group Method of Data Handling (GMDH) type neural network: A case study. Scientific Research and Essay 8(3):120-127.
[11]	Li, G., Ge, J. and Jie, Y. (2003) Free surface seepage analysis based on element free method. Mechanics Research Communications 30(1):9-19.
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[13]	Panthulu, T. V., Krishnaiah, C. and Shirke, J. M. (2001) Detection of seepage paths in earth dams using self potential and electrical resistivity methods. Engineering Geology 59(3-4):281-295.
[14]	Kazemzadeh-Parsi, M. J. and Daneshmand, S. (2011) Unconfined seepage analysis in earth dams using smoothed fixed grid finite element method. International Journal for Numerical and Analytical Methods in Geomechanics 36(1):449-461.
[15]	Chen, Q and Zhang, L. M. (2006) Three dimensional analysis of water infiltration into Gouhou rockfill dam using saturated seepage theory. Canadian Geotechnical. Journal 43(5): 449-461.
[16]	Kermani, E. F. and Barani, G. A. (2012) Seepage Analysis through Earth Dam on Finite Difference Method. Journal of basic and Applied Scientific Research 4(3) 23-61.
[17]	Dupuits, J. (1863) Theoriques et pratiques sur le movement des Eaux dan les Canaux decouverts et a travers les terrains permeables (2nd Ed): Fans: Dunod.
[18]	Schaffernak, F. (1916) Theory of bed transportation and its application 68(12):209-214.
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APA Style

Arinze Emmanuel Emeka, Agunwamba Jonah Chukwuemeka. (2019). Modified Schaffernak’s Solution for Seepage Through Earth Dam. Mathematical Modelling and Applications, 3(4), 44-50. https://doi.org/10.11648/j.mma.20180304.11

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ACS Style

Arinze Emmanuel Emeka; Agunwamba Jonah Chukwuemeka. Modified Schaffernak’s Solution for Seepage Through Earth Dam. Math. Model. Appl. 2019, 3(4), 44-50. doi: 10.11648/j.mma.20180304.11

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AMA Style

Arinze Emmanuel Emeka, Agunwamba Jonah Chukwuemeka. Modified Schaffernak’s Solution for Seepage Through Earth Dam. Math Model Appl. 2019;3(4):44-50. doi: 10.11648/j.mma.20180304.11

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@article{10.11648/j.mma.20180304.11,
  author = {Arinze Emmanuel Emeka and Agunwamba Jonah Chukwuemeka},
  title = {Modified Schaffernak’s Solution for Seepage Through Earth Dam},
  journal = {Mathematical Modelling and Applications},
  volume = {3},
  number = {4},
  pages = {44-50},
  doi = {10.11648/j.mma.20180304.11},
  url = {https://doi.org/10.11648/j.mma.20180304.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20180304.11},
  abstract = {Seepage analysis forms an important and basic part of geotechnical engineering owing to its importance in ground water contamination control, slope stability analysis and dam design. Furthermore, It is important for determining the distribution of seepage uplift pressures and the resulting seepage forces as well as the estimation of the volume of seepage losses through the body and the foundation of earth dams. Casagrande (1940) and Schaffernak (1916) improved on Dupuit’s solution of seepage through earth dam without considering tail water. In this work, modification of Schaffernak’s model was done to accommodate tail water. Values obtained using the new model though similar to that of the three other models (Dupuit, Casagrande and Schaffernak) shows that existence of tail water affects the value of seepage. The new model is very consistent from 3-6 m height. Though the seepage equation from the new model is similar to that of Casagrande, they differ because the value of seepage face for the tail water ‘a’, used for computations are not the same. For each of the model, there is a linear relationship between the seepage and the height of water upsream. Interestingly, there is a sharp change in seepage at 6m height of dam with increase in slope between 6 m and 9 m for each model except at the slope of 1:2.5 where a decrease in slope was recorded for the new model.},
 year = {2019}
}

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TY  - JOUR
T1  - Modified Schaffernak’s Solution for Seepage Through Earth Dam
AU  - Arinze Emmanuel Emeka
AU  - Agunwamba Jonah Chukwuemeka
Y1  - 2019/01/03
PY  - 2019
N1  - https://doi.org/10.11648/j.mma.20180304.11
DO  - 10.11648/j.mma.20180304.11
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 44
EP  - 50
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20180304.11
AB  - Seepage analysis forms an important and basic part of geotechnical engineering owing to its importance in ground water contamination control, slope stability analysis and dam design. Furthermore, It is important for determining the distribution of seepage uplift pressures and the resulting seepage forces as well as the estimation of the volume of seepage losses through the body and the foundation of earth dams. Casagrande (1940) and Schaffernak (1916) improved on Dupuit’s solution of seepage through earth dam without considering tail water. In this work, modification of Schaffernak’s model was done to accommodate tail water. Values obtained using the new model though similar to that of the three other models (Dupuit, Casagrande and Schaffernak) shows that existence of tail water affects the value of seepage. The new model is very consistent from 3-6 m height. Though the seepage equation from the new model is similar to that of Casagrande, they differ because the value of seepage face for the tail water ‘a’, used for computations are not the same. For each of the model, there is a linear relationship between the seepage and the height of water upsream. Interestingly, there is a sharp change in seepage at 6m height of dam with increase in slope between 6 m and 9 m for each model except at the slope of 1:2.5 where a decrease in slope was recorded for the new model.
VL  - 3
IS  - 4
ER  -

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Author Information

Arinze Emmanuel Emeka

Department of Civil Engineering, Michael Okpara University of Agriculture, Umudike, Nigeria
Agunwamba Jonah Chukwuemeka

Department of Civil Engineering, University of Nigeria, Nsukka, Nigeria

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APA Style

Arinze Emmanuel Emeka, Agunwamba Jonah Chukwuemeka. (2019). Modified Schaffernak’s Solution for Seepage Through Earth Dam. Mathematical Modelling and Applications, 3(4), 44-50. https://doi.org/10.11648/j.mma.20180304.11

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ACS Style

Arinze Emmanuel Emeka; Agunwamba Jonah Chukwuemeka. Modified Schaffernak’s Solution for Seepage Through Earth Dam. Math. Model. Appl. 2019, 3(4), 44-50. doi: 10.11648/j.mma.20180304.11

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AMA Style

Arinze Emmanuel Emeka, Agunwamba Jonah Chukwuemeka. Modified Schaffernak’s Solution for Seepage Through Earth Dam. Math Model Appl. 2019;3(4):44-50. doi: 10.11648/j.mma.20180304.11

Copy | Download

@article{10.11648/j.mma.20180304.11,
  author = {Arinze Emmanuel Emeka and Agunwamba Jonah Chukwuemeka},
  title = {Modified Schaffernak’s Solution for Seepage Through Earth Dam},
  journal = {Mathematical Modelling and Applications},
  volume = {3},
  number = {4},
  pages = {44-50},
  doi = {10.11648/j.mma.20180304.11},
  url = {https://doi.org/10.11648/j.mma.20180304.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20180304.11},
  abstract = {Seepage analysis forms an important and basic part of geotechnical engineering owing to its importance in ground water contamination control, slope stability analysis and dam design. Furthermore, It is important for determining the distribution of seepage uplift pressures and the resulting seepage forces as well as the estimation of the volume of seepage losses through the body and the foundation of earth dams. Casagrande (1940) and Schaffernak (1916) improved on Dupuit’s solution of seepage through earth dam without considering tail water. In this work, modification of Schaffernak’s model was done to accommodate tail water. Values obtained using the new model though similar to that of the three other models (Dupuit, Casagrande and Schaffernak) shows that existence of tail water affects the value of seepage. The new model is very consistent from 3-6 m height. Though the seepage equation from the new model is similar to that of Casagrande, they differ because the value of seepage face for the tail water ‘a’, used for computations are not the same. For each of the model, there is a linear relationship between the seepage and the height of water upsream. Interestingly, there is a sharp change in seepage at 6m height of dam with increase in slope between 6 m and 9 m for each model except at the slope of 1:2.5 where a decrease in slope was recorded for the new model.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Modified Schaffernak’s Solution for Seepage Through Earth Dam
AU  - Arinze Emmanuel Emeka
AU  - Agunwamba Jonah Chukwuemeka
Y1  - 2019/01/03
PY  - 2019
N1  - https://doi.org/10.11648/j.mma.20180304.11
DO  - 10.11648/j.mma.20180304.11
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 44
EP  - 50
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20180304.11
AB  - Seepage analysis forms an important and basic part of geotechnical engineering owing to its importance in ground water contamination control, slope stability analysis and dam design. Furthermore, It is important for determining the distribution of seepage uplift pressures and the resulting seepage forces as well as the estimation of the volume of seepage losses through the body and the foundation of earth dams. Casagrande (1940) and Schaffernak (1916) improved on Dupuit’s solution of seepage through earth dam without considering tail water. In this work, modification of Schaffernak’s model was done to accommodate tail water. Values obtained using the new model though similar to that of the three other models (Dupuit, Casagrande and Schaffernak) shows that existence of tail water affects the value of seepage. The new model is very consistent from 3-6 m height. Though the seepage equation from the new model is similar to that of Casagrande, they differ because the value of seepage face for the tail water ‘a’, used for computations are not the same. For each of the model, there is a linear relationship between the seepage and the height of water upsream. Interestingly, there is a sharp change in seepage at 6m height of dam with increase in slope between 6 m and 9 m for each model except at the slope of 1:2.5 where a decrease in slope was recorded for the new model.
VL  - 3
IS  - 4
ER  -

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