8/8/2019 7 Permeability ZU

1/30

1

Field Tests

Permeable soil formations are those that permitmovement of appreciable quantities of water. Inthis case it is called an aquifer.

If the permeability is very low or practicallyimpermeable it is called an Aquitard

. .

.

8/8/2019 7 Permeability ZU

2/30

2

AquifersAquifers

Free groundwater tableFree groundwater tableunder atmosphericunder atmospheric

pressurepressure

Groundwater is confinedGroundwater is confinedbetween two impermeablebetween two impermeable

layerslayers

(2) Confined(2) Confined(1) Unconfined(1) Unconfined

Aquifer (unconfined)Confined portion

Unocnfined

portion

Recharge

Recharge

Recharge

Water Table

8/8/2019 7 Permeability ZU

3/30

3

8/8/2019 7 Permeability ZU

4/30

4

Estimating k from unconfined pumping test

Q

Pump

Well

Original GWT

Observation wells

h1

h2

Impervious stratumr1

r2

rhdr

dhk

AikQ

T2..

..

!

!

!2

1

2

1

.2

h

h

r

r

dhhQ

k

r

dr T

21221

2

ln.

hh

r

r

Qk

!T

8/8/2019 7 Permeability ZU

5/30

5

Estimating k from confined pumping test

Q

Pump

Well

Original GWT

Observation wells

h1h2

Impervious stratumr1

r2

rDdr

dhk

AikQ

T2..

..

!

!

!2

1

2

1

2h

h

r

r

dhQ

kD

r

dr T

121

2ln

.2 hh

r

r

k

!T

Impervious stratum

AquiferD

8/8/2019 7 Permeability ZU

6/30

6

8/8/2019 7 Permeability ZU

7/30

7

8/8/2019 7 Permeability ZU

8/30

8

8/8/2019 7 Permeability ZU

9/30

9

8/8/2019 7 Permeability ZU

10/30

10

Permeability of stratified soils

+ water =

Compactive

effort

8/8/2019 7 Permeability ZU

11/30

11

+ water =

Compactive

effort

Average permeability in Horizontal Direction

Let H1, H2 etc. be the thickness of soil layers having permeabilitycoefficient k1, k2 etc. For the flow in the horizontal direction, thehydraulic gradient (i) will be the same for all layers.

8/8/2019 7 Permeability ZU

12/30

12

+ water =

Compactive

effort

However, since v = k . i , and since k is different, the velocityof flow will be different in different layers.

Let (kI) be the average permeability of the soil in thehorizontal direction.

The total discharge through the soil equals the sum ofdischarges through the individual layers, i.e.:q = kI . I . H = k1 . i . H1 + k2 . i . H2 + k3 . i . H3+Take: H = H1 + H2 + H3 +

8/8/2019 7 Permeability ZU

13/30

13

Average permeability in Horizontal Direction

In this case, the velocity of flow and hence the discharge will be thesame through each layer but the hydraulic gradient will be different.

Assuming that the head loss for the different layers is h1, h2, h3 etc. and the total head loss is (h), we have:

8/8/2019 7 Permeability ZU

14/30

14

8/8/2019 7 Permeability ZU

15/30

15

Two Dimensional Flow of Water Through PorousMediaConsider an element of soil shown with a unit thickness (perpendicular to theplane of the paper). The velocity of water entering the element, and the exitvelocities will be as shown in the figure.

In Flow = Out flow

8/8/2019 7 Permeability ZU

16/30

16

This is the Continuity Equation for 2-D

flow

where: kx and ky are the coefficients of permeability in the xand y directions, respectively. Substituting in Equation A,

A

8/8/2019 7 Permeability ZU

17/30

17

This is Laplace Equation of2-D flow of water throughporous media

Solution of this differential equation requires knowledge of

the boundary conditions.B/C for real structures are complexNo analytical or closed form solution can be found

8/8/2019 7 Permeability ZU

18/30

18

Approximate Solutions

1) Flow net sketching2) Finite difference

Flow net is a graphical representation of a flow field thatsatisfies Laplaces Eq. and comprises a family of flowlines and equipotential lines and is based on trialsketching.

8/8/2019 7 Permeability ZU

19/30

19

Properties of flow nets:(a) Boundary conditions must be satisfied

(b) The flow lines and equal-potential lines must intersect atright angles.

(c) Area between flow lines and potential lines must becurve-linear squares.

(d) All curves should be smooth.(e) Flow lines cannot intersect each other(f) Equipotential lines cannot intersect each other(g) The number of flow channels is usually not less than 5.

8/8/2019 7 Permeability ZU

20/30

20

8/8/2019 7 Permeability ZU

21/30

21

8/8/2019 7 Permeability ZU

22/30

22

8/8/2019 7 Permeability ZU

23/30

23

Example of a flow net

Note that:(a) Lines JJ1 and FF1 are equi-potential lines.

(b) Line ABCDEF is a flow line(c) Line I-I is a flow line(d) Flow lines and equi-potential lines are mostly perpendicular(e) Fields are mostly square(f) All lines are smooth.

8/8/2019 7 Permeability ZU

24/30

24

Let (h = head drop through the field and(

q = discharge passing through the flow channelH = total pressure head.

Applying Darcys law q = k .i .A

)1.(bL

hkq (!(

Let: Nd = number of head drops and Nf = number of flow

channels

)(Nd

bHkq !(

8/8/2019 7 Permeability ZU

25/30

25

For square mesh b/L = 1 , therefore)(Nd

bHkq !(

d

f

d N

NHkqandN

Hkq ..,. !!(

Nf = 6Nd = 24If k = 1 x 10-3 cm/sec, andH = 3 m

8/8/2019 7 Permeability ZU

26/30

26d

f

d N

NHkqand

N

Hkq

..,

.!!(

8/8/2019 7 Permeability ZU

27/30

27

Cofferdam

8/8/2019 7 Permeability ZU

28/30

28

Protective Filters

8/8/2019 7 Permeability ZU

29/30

29

Protective Filters

D15 Filter > 4D15 Soil

D15 Filter < 4D85

Soil

8/8/2019 7 Permeability ZU

30/30

30

Protective Filters

D15 Filter > 4D15 Soil

D15 Filter < 4D85