A simple approach for seepage through earthen made dams analysis based on finite differences modelling

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
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3. DAMS ?
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4. EARTHEN MADE DAMS
 Dams made with heavily compacted
earthen materials (sand, clay, silt,…)
 Convenient to retain a low water height
(<= 10 m)
 Cheap ()
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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
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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
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7. EVALUATING SEEPAGE
(ACTUAL METHODS)
• The hydraulic method : 𝑞 = 𝑘𝐻𝑖
• Kozeny’s parabola
𝑦0 =
𝑑 2 + ℎ2 − 𝑑 𝑡ℎ𝑒𝑛 𝑞 = 𝑘𝑦0
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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
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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
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10. ENGINEERING EXAMPLE
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11. ENGINEERING EXAMPLE (Cont’d)
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12. PERSPECTIVES FOR FURTHER RESEARCH
• Benchmark (efficiency, accuracy)
against FE, FV methods
• Investigate
anisotropic
structure models
dam
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