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

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

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

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

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

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 SHELL SHELL blanket
CORE
SHELL
SHELL
blanket
FOUNDATION
cutoff

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

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

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

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

15. Quick Condition in Granular Soils
During upward flow, at X:
flow hw L X
soil z hL
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. 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 hL
datum
TH = hL
TH = 0

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

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

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

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

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

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. 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
typically 5-6

24. Piping Failures
Baldwin Hills Dam after it failed by piping in 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.

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 Design
Two major criteria:
granular filter
(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. Granular Filter Design
Retention criteria:
Permeability criteria:
D15, filter < 5 D85, soil
D15, filter > 4 D15, soil
average filter pore size
- 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. Drainage Provisions in Retaining Walls
weep hole
geosynthetics
granular soil
drain pipe