1 permeability and seepage n. sivakugan duration = 17 minutes
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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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Bernoulli’s Equation
1. Kinetic energy
datum
z
fluid particle
The energy of a fluid particle is made of:
2. Strain energy
3. Potential energy
- due to velocity
- due to pressure
- due to elevation (z) with respect to a datum
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Bernoulli’s Equation
Total head =
datum
z
fluid particle
Expressing energy in unit of length:
Velocity head
+
Pressure head
+
Elevation head
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Bernoulli’s Equation
Total head =
datum
z
fluid particle
For flow through soils, velocity (and thus velocity head) is very small. Therefore,
Velocity head
+
Pressure head
+
Elevation head
0
Total head = Pressure head + Elevation head
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Some NotesIf 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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Some Notes
Pressure head = pore water pressure/w
Elevation head = height above the selected datum
At any point within the flow regime:
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Some Notes
Hydraulic gradient (i) between A and B is the total head loss per unit length.
water
A BAB
BA
l
THTHi
length AB, along the stream line
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Darcy’s LawVelocity (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)10-310-6 100
clays gravelssandssilts
CoarseFines
For coarse grain soils, k = f(e or D10)
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Stresses due to Flow
X
soil
hw
L
Static Situation (No flow)
zv = whw + satz
u = w (hw + z)
v ' = ' z
At X,
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Stresses due to FlowDownward Flow
hw
L
flow
X
soil
z
v = whw + satz
w hw + w(L-hL)(z/L)
v ' = ' z + wiz
At X,
hL
u = w hw
u = w (hw+L-hL)
… as for static case
= w hw + w(z-iz)
= w (hw+z) - wiz
Reduction due to flow
Increase due to flow
u =
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Stresses due to Flow
flow
Upward Flow
hw
LX
soil
z
v = whw + satz
w hw + w(L+hL)(z/L)
v ' = ' z - wiz
At X,
hL
u = w hw
u = w (hw+L+hL)
… as for static case
= w hw + w(z+iz)
= w (hw+z) + wiz
Increase due to flow
Reduction due to flow
u =
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Quick Condition in Granular SoilsDuring upward flow, at X:
v ' = ' z - wiz
flow
hw
LX
soil
z
hL
izw
w '
Critical hydraulic gradient (ic)
If i > ic, the effective stresses is negative.
i.e., no inter-granular contact & thus failure.
- Quick condition
Seepage Terminology
concrete dam
impervious strata
soil
Stream line is simply the path of a water molecule.
datum
hL
TH = 0TH = hL
From upstream to downstream, total head steadily decreases along the stream line.
Seepage TerminologyEquipotential line is simply a contour of constant total head.
concrete dam
impervious strata
soil
datum
hL
TH = 0TH = hL
TH=0.8 hL
FlownetA network of selected stream lines and equipotential lines.
concrete dam
impervious strata
soil
curvilinear square
90º
Quantity of Seepage (Q)
d
fL N
NkhQ ….per unit length normal to the plane
# of flow channels
# of equipotential drops
impervious strata
concrete dam
hL
head loss from upstream to downstream
Heads at a Point X
impervious strata
concrete dam
datum
X
z
hL
TH = hL TH = 0
Total head = hL - # of drops from upstream x h
h
Elevation head = -z
Pressure head = Total head – Elevation headd
L
N
h
Piping in Granular Soils
datumconcrete dam
impervious strata
soil
hL
At the downstream, near the dam,
h = total head dropl
l
hiexit
the exit hydraulic gradient
Piping in Granular Soils
datumconcrete dam
impervious strata
soil
hL
If iexit exceeds the critical hydraulic gradient (ic), firstly
the soil grains at exit get washed away.
no soil; all water
This phenomenon progresses towards the upstream, forming a free passage of water (“pipe”).
Piping in Granular SoilsPiping is a very serious problem. It leads to downstream flooding which can result in loss of lives.
concrete dam
impervious strata
soil
Therefore, provide adequate safety factor against piping.
exit
cpiping i
iF
typically 5-6
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Piping FailuresBaldwin 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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FiltersUsed 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 DesignTwo major criteria:
(a) Retention Criteria
(b) Permeability Criteria
- to prevent washing out of fines
- to facilitate drainage and thus avoid build-up of pore pressures
Filter grains must not be too coarse
Filter grains must not be too fine
granular filter
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Granular Filter DesignRetention criteria:
D15, filter < 5 D85, soil
- after Terzaghi & Peck (1967)
Permeability criteria:
D15, filter > 4 D15, soil
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
Drainage Provisions in Retaining Walls
drain pipe
granular soil
weep hole
geosynthetics