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# Permeability sivakugan (Complete Soil Mech. Undestanding Pakage: ABHAY)

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Complete Soil Mech. Undestanding Pakage: ABHAY)

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### Permeability sivakugan (Complete Soil Mech. Undestanding Pakage: ABHAY)

1. 1. 1 Permeability and Seepage N. Sivakugan Duration = 17 minutes
2. 2. Copyright©2001 SIVA 2 What is permeability? A measure of how easily a fluid (e.g., water) can pass through a porous medium (e.g., soils) Loose soil - easy to flow - high permeability Dense soil - difficult to flow - low permeability water
3. 3. Copyright©2001 SIVA fluid particle 3 Bernoulli’s Equation 1. Kinetic energy datum z The energy of a fluid particle is made of: - due to velocity 2. Strain energy - due to pressure 3. Potential energy - due to elevation (z) with respect to a datum
6. 6. Copyright©2001 SIVA 6 Some Notes If flow is from A to B, total head is higher at A than at B. water A B Energy is dissipated in overcoming the soil resistance and hence is the head loss.
7. 7. Copyright©2001 At any point within the flow regime: SIVA 7 Some Notes Pressure head = pore water pressure/gw Elevation head = height above the selected datum
8. 8. Copyright©2001 SIVA 8 Some Notes Hydraulic gradient (i) between A and B is the total head loss per unit length. water A B i = TH - TH A B l AB length AB, along the stream line
9. 9. Copyright©2001 SIVA 9 Darcy’s Law Velocity (v) of flow is proportional to the hydraulic gradient (i) – Darcy (1856) v = k i Permeability • or hydraulic conductivity • unit of velocity (cm/s)
10. 10. Copyright©2001 SIVA 10 Large Earth Dam SHELL FOUNDATION SHELL CORE blanket filter cutoff crest riprap free board
11. 11. Copyright©2001 SIVA 11 Permeability Values (cm/s) 10-6 10-3 100 clays silts sands gravels Fines Coarse For coarse grain soils, k = f(e or D10)
12. 12. Copyright©2001 Static Situation (No flow) SIVA 12 Stresses due to Flow X soil hw L z At X, s= gh+ gz v ww satu = g(h+ z) w w s' = g' z v
13. 13. Copyright©2001 Stresses due to Flow Downward Flow At X, SIVA hw L flow z X soil sv = gwhw + gsatz gw hw + gw(L-hL)(z/L) sv ' = g' z + gwiz hL u = gw hw u = gw (hw+L-hL) … as for static case = gw hw + gw(z-iz) = gw (hw+z) - gwiz Reduction due to flow Increase due to flow u =
14. 14. Copyright©2001 At X, SIVA 14 Stresses due to Flow flow Upward Flow hw L z X soil sv = gwhw + gsatz gw hw + gw(L+hL)(z/L) sv ' = g' z - gwiz hL u = gw hw u = gw (hw+L+hL) … as for static case = gw hw + gw(z+iz) = gw (hw+z) + gwiz Increase due to flow Reduction due to flow u =
15. 15. Copyright©2001 Quick Condition in Granular Soils During upward flow, at X: sv SIVA 15 ' = g' z - gwiz flow hw L z X soil hL þ ý ü î í ì g g ' = z - i w g w Critical hydraulic gradient (ic) If i > ic, the effective stresses is negative. i.e., no inter-granular contact & thus failure. - Quick condition
16. 16. Seepage Terminology Stream line is simply the path of a water molecule. From upstream to downstream, total head steadily decreases along the stream line. concrete dam impervious strata soil datum hL TH = h TH = 0 L
17. 17. Seepage Terminology Equipotential line is simply a contour of constant total head. concrete dam impervious strata soil datum hL TH = h TH = 0 L TH=0.8 hL
18. 18. Flownet A network of selected stream lines and equipotential lines. concrete dam impervious strata soil curvilinear square 90º
19. 19. Quantity of Seepage (Q) f Q = kh ….per unit length normal to the plane d N L N # of flow channels # of equipotential drops concrete dam impervious strata hL head loss from upstream to downstream
20. 20. Heads at a Point X = h Elevation head = -z Pressure head = Total head – Elevation head d TH = hL TH = 0 concrete dam impervious strata hL datum z X Total head = hL - # of drops from upstream x Dh Dh L N
21. 21. Piping in Granular Soils datum concrete dam impervious strata soil hL At the downstream, near the dam, i h exit D Dh = total head drop Dl l = D the exit hydraulic gradient
22. 22. Piping in Granular Soils If iexit exceeds the critical hydraulic gradient (ic), firstly the soil grains at exit get washed away. This phenomenon progresses towards the upstream, forming a free passage of water (“pipe”). datum concrete dam impervious strata soil hL no soil; all water
23. 23. Piping in Granular Soils Piping is a very serious problem. It leads to downstream flooding which can result in loss of lives. Therefore, provide adequate safety factor against piping. concrete dam impervious strata soil F = i c piping i exit typically 5-6
24. 24. Copyright©2001 SIVA 24 Piping Failures Baldwin Hills Dam after it failed by piping in 1963. The failure occurred when a concentrated leak developed along a crack in the embankment, eroding the embankment fill and forming this crevasse. An alarm was raised about four hours before the failure and thousands of people were evacuated from the area below the dam. The flood that resulted when the dam failed and the reservoir was released caused several millions of dollars in damage.