1 Permeability and Seepage N. Sivakugan Duration = 17 minutes

Permeability and Seepage

N. Sivakugan

Duration = 17 minutes

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

Bernoulli’s Equation

1. Kinetic energy

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

Total head =

fluid particle

Expressing energy in unit of length:

Velocity head

Pressure head

Elevation head

Total head =

fluid particle

For flow through soils, velocity (and thus velocity head) is very small. Therefore,

Velocity head

Pressure head

Elevation head

Total head = Pressure head + Elevation head

Some NotesIf 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.

Some Notes

Pressure head = pore water pressure/w

Elevation head = height above the selected datum

At any point within the flow regime:

Some Notes

Hydraulic gradient (i) between A and B is the total head loss per unit length.

length AB, along the stream line

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)

10SIVA

Large Earth Dam

FOUNDATION

blanket

filter

cutoff

riprap

free board

11SIVA

Permeability Values (cm/s)10-310-6 100

clays gravelssandssilts

CoarseFines

For coarse grain soils, k = f(e or D10)

12SIVA

Stresses due to Flow

Static Situation (No flow)

zv = whw + satz

u = w (hw + z)

v ' = ' z

Stresses due to FlowDownward Flow

v = whw + satz

w hw + w(L-hL)(z/L)

v ' = ' z + wiz

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

14SIVA

Stresses due to Flow

Upward Flow

v = whw + satz

w hw + w(L+hL)(z/L)

v ' = ' z - wiz

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

15SIVA

Quick Condition in Granular SoilsDuring upward flow, at X:

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

Seepage Terminology

concrete dam

impervious strata

Stream line is simply the path of a water molecule.

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

TH = 0TH = hL

TH=0.8 hL

FlownetA network of selected stream lines and equipotential lines.

concrete dam

impervious strata

curvilinear square

Quantity of Seepage (Q)

NkhQ ….per unit length normal to the plane

# of flow channels

# of equipotential drops

impervious strata

concrete dam

head loss from upstream to downstream

Heads at a Point X

impervious strata

concrete dam

TH = hL TH = 0

Total head = hL - # of drops from upstream x h

Elevation head = -z

Pressure head = Total head – Elevation headd

Piping in Granular Soils

datumconcrete dam

impervious strata

At the downstream, near the dam,

h = total head dropl

hiexit

the exit hydraulic gradient

Piping in Granular Soils

datumconcrete dam

impervious strata

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

Therefore, provide adequate safety factor against piping.

cpiping i

typically 5-6

24SIVA

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.

25SIVA

Piping Failures

Fontenelle Dam, USA (1965)

26SIVA

FiltersUsed for:

facilitating drainage preventing fines from being washed away

Used in: earth dams

retaining walls

Filter Materials: granular soils

geotextiless

27SIVA

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

28SIVA

Granular Filter DesignRetention criteria:

D15, filter < 5 D85, soil

- after Terzaghi & Peck (1967)

Permeability criteria:

D15, filter > 4 D15, soil

average filter pore size

- 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

1 Permeability and Seepage N. Sivakugan Duration = 17 minutes

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