Complete Soil Mech. Undestanding Pakage: ABHAY)

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

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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

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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

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

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

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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.

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

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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

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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)

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

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

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Static Situation (No flow)
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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. Copyright©2001 Stresses due to Flow
Downward Flow
At X,
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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 =

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At X,
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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 =

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Quick Condition in Granular Soils
During upward flow, at X:
sv
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' = 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. 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. 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. Flownet
A network of selected stream lines and equipotential
lines.
concrete dam
impervious strata
soil
curvilinear
square
90º

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. 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. 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. 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
F = i
c
piping i
exit
typically 5-6

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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.

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Piping Failures
Fontenelle Dam, USA (1965)

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

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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
granular filter

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

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