Permeability and Seepage

1. Permeability and Seepage N. Sivakugan Duration = 17 minutes

2. What is permeability? A measure of how easily a fluid (e.g., water) can pass through a porous medium (e.g., soils) water Loose soil - easy to flow - high permeability Dense soil - difficult to flow - low permeability

3. fluid particle z datum Bernoulli’s Equation The energy of a fluid particle is made of: 1. Kinetic energy - due to velocity 2. Strain energy - due to pressure 3. Potential energy - due to elevation(z) with respect to a datum

4. fluid particle z datum Bernoulli’s Equation Expressing energy in unit of length: Total head = Velocity head + Pressure head + Elevation head

5. 0 fluid particle z datum Bernoulli’s Equation For flow through soils, velocity (and thus velocity head) is very small. Therefore, Total head = Velocity head + Pressure head + Elevation head Total head = Pressure head + Elevation head

6. water B A Some Notes If flow is from A to B, total head is higher at A than at B. Energy is dissipated in overcoming the soil resistance and hence is the head loss.

7. Some Notes At any point within the flow regime: Pressure head = pore water pressure/w Elevation head = height above the selected datum

8. water B A length AB, along the stream line Some Notes Hydraulic gradient (i) between A and B is the total head loss per unit length.

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. Large Earth Dam crest filter free board riprap CORE SHELL SHELL blanket FOUNDATION cutoff

11. 10-6 10-3 100 clays silts sands gravels Coarse Fines Permeability Values (cm/s) For coarse grain soils, k = f(e or D10)

12. hw z L X soil Stresses due to Flow Static Situation (No flow) At X, v = whw + satz u = w (hw + z) v ' = ' z

13. flow u = w hw hw hL z L X soil Reduction due to flow u = w (hw+L-hL) Increase due to flow Stresses due to Flow Downward Flow At X, v = whw + satz … as for static case w hw + w(L-hL)(z/L) u = = w hw + w(z-iz) = w (hw+z) - wiz v ' = ' z + wiz

14. flow hL hw u = w hw z L X soil Increase due to flow u = w (hw+L+hL) Reduction due to flow Stresses due to Flow Upward Flow At X, v = whw + satz … as for static case w hw + w(L+hL)(z/L) u = = w hw + w(z+iz) = w (hw+z) + wiz v ' = ' z - wiz

15. flow hL hw z L X soil Quick Condition in Granular Soils During upward flow, at X: v ' = ' z - wiz Critical hydraulic gradient (ic) If i > ic, the effective stresses is negative. i.e., no inter-granular contact & thus failure. - Quick condition

16. hL datum concrete dam soil impervious strata Seepage Terminology Stream line is simply the path of a water molecule. From upstream to downstream, total head steadily decreases along the stream line. TH = hL TH = 0

17. hL datum concrete dam TH = hL TH = 0 soil impervious strata Seepage Terminology Equipotential line is simply a contour of constant total head. TH=0.8 hL

18. concrete dam curvilinear square 90º soil impervious strata Flownet A network of selected stream linesand equipotential lines.

19. # of flow channels # of equipotential drops head loss from upstream to downstream hL concrete dam impervious strata Quantity of Seepage (Q) ….per unit length normal to the plane

20. hL datum concrete dam z h X impervious strata Heads at a Point X Total head = hL - # of drops from upstream x h Elevation head = -z Pressure head = Total head – Elevation head TH = hL TH = 0

21. hL datum concrete dam l h = total head drop soil impervious strata Piping in Granular Soils At the downstream, near the dam, the exit hydraulic gradient

22. hL datum concrete dam no soil; all water soil impervious strata 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”).

23. concrete dam typically 5-6 soil impervious strata 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.

24. 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. Piping Failures

25. Piping Failures Fontenelle Dam, USA (1965)

26. Filters Used for: • facilitating drainage • preventing fines from being washed away Used in: Filter Materials: • earth dams • granular soils • retaining walls • geotextiless

27. granular filter Granular Filter Design Two major criteria: (a) Retention Criteria - to prevent washing out of fines  Filter grains must not be too coarse (b) Permeability Criteria - to facilitate drainage and thus avoid build-up of pore pressures  Filter grains must not be too fine

28. average filter pore size Granular Filter Design Retention criteria: Permeability criteria: D15, filter < 5 D85, soil D15, filter > 4 D15, soil - after Terzaghi & Peck (1967) D15, filter < 20 D15, soil - after US Navy (1971) D50, filter < 25 D50, soil GSD Curves for the soil and filter must be parallel

29. weep hole geosynthetics granular soil drain pipe Drainage Provisions in Retaining Walls