Transcript Document

Permeability and Seepage
N. Sivakugan
Duration = 17 minutes
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Copyright©2001
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
Dense soil
- easy to flow
- difficult to flow
- high permeability
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- low permeability 2
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Bernoulli’s Equation
The energy of a fluid particle is
made of:
1. Kinetic energy
fluid particle
- due to velocity
2. Strain energy
z
- due to pressure
datum
3. Potential energy
- due to elevation (z) with respect to a datum
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Bernoulli’s Equation
Expressing energy in unit of length:
Velocity head
+
fluid particle
z
Total head =
Pressure head
+
datum
Elevation head
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Bernoulli’s Equation
For flow through soils, velocity (and thus
velocity head) is very small. Therefore,
Velocity head
+
0
fluid particle
z
Total head =
Pressure head
+
datum
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.
Energy is dissipated in
overcoming the soil
resistance and hence
is the head loss.
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water
A
B
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Some Notes
At any point within the flow regime:
Pressure head = pore water pressure/w
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.
TH A  TH B
i
l AB
water
A
B
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=ki
Permeability
• or hydraulic conductivity
• unit of velocity (cm/s)
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Large Earth Dam
crest
free board
filter
riprap
CORE
SHELL
SHELL
blanket
cutoff
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FOUNDATION
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Permeability Values (cm/s)
10-6
clays
10-3
silts
Fines
100
sands
gravels
Coarse
For coarse grain soils, k = f(e or D10)
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Stresses due to Flow
Static Situation (No flow)
hw
L
At X,
z
X
soil
v = whw + satz
u = w (hw + z)
v ' = ' z
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Stresses due to Flow
Downward Flow
At X,
v = whw + satz
flow
… as for static case
u = w hw + w(L-hL)(z/L)
hL
= w hw + w(z-iz)
= w (hw+z) - wiz
u = w h w
hw
L
z
X
soil
Reduction due to flow
v ' = ' z + wiz
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Increase due to flow
u = w (hw+L-hL)
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Stresses due to Flow
Upward Flow
flow
At X,
v = whw + satz
… as for static case
u = w hw + w(L+hL)(z/L)
hL
= w hw + w(z+iz)
= w (hw+z) + wiz
u = w h w
hw
L
z
X
soil
Increase due to flow
v ' = ' z - wiz
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u = w (hw+L+hL)
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Reduction due to flow
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Quick Condition in Granular Soils
During upward flow, at X:
v ' = ' z - wiz
' 
  wz  i
 w 
flow
hL
hw
Critical hydraulic gradient (ic)
L
If i > ic, the effective stresses is negative.
z
X
soil
i.e., no inter-granular contact & thus failure.
- Quick condition
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Seepage Terminology
Stream line is simply the path of a water molecule.
From upstream to downstream, total head steadily decreases
along the stream line.
hL
datum
TH = hL
concrete dam
TH = 0
soil
impervious strata
Seepage Terminology
Equipotential line is simply a contour of constant
total head.
hL
datum
TH = hL
concrete dam
TH=0.8 hL
impervious strata
TH = 0
soil
Flownet
A network of selected stream lines and equipotential
lines.
concrete dam
curvilinear
square
90º
impervious strata
soil
Quantity of Seepage (Q)
Q  khL
Nf
Nd
# of flow channels
….per unit length normal to the plane
# of equipotential drops
head loss from upstream to
downstream
hL
concrete
dam
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
hL

Nd
hL
TH = hL
concrete
dam
datum
TH = 0
z
h
X
impervious strata
Piping in Granular Soils
At the downstream, near the dam,
the exit hydraulic gradient
iexit
h

l
hL
datum
concrete
dam
l
soil
impervious strata
h = total head drop
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”).
hL
datum
concrete
dam
no soil; all water
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.
Fpiping 
concrete
dam
iexit
typically 5-6
soil
impervious strata
ic
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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
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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
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Filter Materials:
 granular soils

geotextiless
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Granular Filter Design
Two major criteria:
(a)
granular filter
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
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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
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Drainage Provisions in Retaining Walls
weep hole
geosynthetics
granular soil
drain pipe