05 Permeability

Permeability and Seepage

2

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

3

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

4

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

6

Some NotesIf flow is from A to B, total head is higher at A

than at B.

water

AB

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

AB

AB

BA

lTHTHi

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)

z

v = whw + satz

u = w (hw + z)

v ' = ' z

At X,

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,

hLu = 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 =

15

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 NN

khQ ….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

Nh

Piping in Granular Soils

datumconcrete dam

impervious strata

soil

hL

At the downstream, near the dam,

h = total head dropl

lhiexit

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.

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