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Numerical methods
for seepage
through earthen
dams analysis
Roland YONABA, Research Assistant
Presented at Cape Coast University
August, July the 19th, 2013
PRESENTATION OUTLINE
• Dams ?
• Earthen-made dams (& facts)
• Overview of the seepage phenomenon
• The research problem
• Perspectives for further research
2
DAMS ?

3
EARTHEN MADE DAMS
 Dams made with heavily compacted
earthen materials (sand, clay, silt,…)
 Convenient to retain a low water height
(<= 10 m)
 Cheap ()
4
EARTHEN DAMS FACTS (IN B.F.)
• Since 1920. Common uses
– irrigation
– water supply
– cattle watering
• Almost 2000 dams in Burkina Faso nowadays
• Quite all of them are earthen-made
5
THE SEEPAGE PROBLEM
• Wet areas downstream ARE NOT natural
springs. Usually.
• Water always follows the path of least
resistance.
–Carry material throughout the dam
–Erosion → Collapse
6
EVALUATING SEEPAGE
(ACTUAL METHODS)

• The hydraulic method : 𝑞 = 𝑘𝐻𝑖
• Kozeny’s parabola
𝑦0 =
𝑑 2 + ℎ2 − 𝑑 𝑡ℎ𝑒𝑛 𝑞 = 𝑘𝑦0

7
HOW CAN WE ACCURATELY EVALUATE
SEEPAGE ?
• Numerical models solve propagative motions

• Types of numerical methods
• Finite Volumes (3D space)
• Finite Elements and Finite Differences (2D
space)

• Why Finite Differences ?
– Fast setup for modelling
8
HOW CAN WE ACCURATELY EVALUATE
SEEPAGE ? (Cont’d)
• General objective
– Build a general purpose model that can predict
headline, pressure, flow distribution and evaluate
seepage quantities through an earthen dam.

• Assumptions
– Soil is uncompressible and isotropic
– Flow is steady and laminar : Darcy’s Law
applies
9
ENGINEERING EXAMPLE

10
ENGINEERING EXAMPLE (Cont’d)

11
PERSPECTIVES FOR FURTHER RESEARCH

• Benchmark (efficiency, accuracy)
against FE, FV methods
• Investigate
anisotropic
structure models

dam

12
Seepage through earthen made dams

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Seepage through earthen made dams

  • 1. Numerical methods for seepage through earthen dams analysis Roland YONABA, Research Assistant Presented at Cape Coast University August, July the 19th, 2013
  • 2. PRESENTATION OUTLINE • Dams ? • Earthen-made dams (& facts) • Overview of the seepage phenomenon • The research problem • Perspectives for further research 2
  • 4. EARTHEN MADE DAMS  Dams made with heavily compacted earthen materials (sand, clay, silt,…)  Convenient to retain a low water height (<= 10 m)  Cheap () 4
  • 5. EARTHEN DAMS FACTS (IN B.F.) • Since 1920. Common uses – irrigation – water supply – cattle watering • Almost 2000 dams in Burkina Faso nowadays • Quite all of them are earthen-made 5
  • 6. THE SEEPAGE PROBLEM • Wet areas downstream ARE NOT natural springs. Usually. • Water always follows the path of least resistance. –Carry material throughout the dam –Erosion → Collapse 6
  • 7. EVALUATING SEEPAGE (ACTUAL METHODS) • The hydraulic method : 𝑞 = 𝑘𝐻𝑖 • Kozeny’s parabola 𝑦0 = 𝑑 2 + ℎ2 − 𝑑 𝑡ℎ𝑒𝑛 𝑞 = 𝑘𝑦0 7
  • 8. HOW CAN WE ACCURATELY EVALUATE SEEPAGE ? • Numerical models solve propagative motions • Types of numerical methods • Finite Volumes (3D space) • Finite Elements and Finite Differences (2D space) • Why Finite Differences ? – Fast setup for modelling 8
  • 9. HOW CAN WE ACCURATELY EVALUATE SEEPAGE ? (Cont’d) • General objective – Build a general purpose model that can predict headline, pressure, flow distribution and evaluate seepage quantities through an earthen dam. • Assumptions – Soil is uncompressible and isotropic – Flow is steady and laminar : Darcy’s Law applies 9
  • 12. PERSPECTIVES FOR FURTHER RESEARCH • Benchmark (efficiency, accuracy) against FE, FV methods • Investigate anisotropic structure models dam 12