lecture 6 flow of water part2 stratifiedsoil

8/10/2019 Lecture 6 Flow of Water Part2 Stratifiedsoil

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Lecture 6 Flow water through

Fl w f Wat r Thr h S il c nt

_

1. Factors affecting permeability

2. Permeability of stratified soil deposits

. or zon a ermea yii. Vertical permeability

3. Quick Condition & Critical hydraulic gradient

Prepared by:

1

a sa ma eng.un mas.my


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Grain size or article size Properties of pore fluid Void ratio of the soil Structural arrange of fabric of the soil particle

Adsorbed water in clayey soil

prepared by:[email protected] 2


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2) Permeability of Stratified Soil Deposits In nature, soils may stratified by the

de osition of la ers which ossess different

permeability characteristics Their beddin ma be horizontal inclined or

vertical. The average permeability used by engineer for

represent the whole deposit will depend uponthe direction of flow with relation to the

rect on o e ng p anes.



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Head lost between the entry & exit faces will

be the same for each la er h 1= h 2 = h 3 = h

,i1= i 2 = i 3 = i

,different layers since v = ki as k is different



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Hence,

o a sc arge sum o sc arge rougthrough soil deposit = individual layers

q = q 1 + q 2 + q 3+ q 4

H 1 1 2 2 3 3 4 4

Or, k = k z + k z + k z + k z z

Where

z = z 1 + z 2 + z 3 + z 4



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The rate of flow will be the same foreac ayer

q1= q 2 = q 3 = q vHowever, the hydraulic gradient, i &head loss, h will be different in differentlayers.



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If h 1, h 2, h 3, h 4 are the loss of heads in each layers,

, Total head loss, h = h 1 + h 2 + h 3 + h 4 But, h 1 = i 1 z1; h 2 = i 2 z2; h 3 = i 3z3 and h 4 = i 4z4

So , h = i 1 z1 + i 2 z 2 + i 3 z 3 + i 4 z 4


Figure 2: Vertical flow


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If k z = average permeability perpendicular to the

, v = k z i = k z. h/z Or, vvvvvz

From head loss, obtained4

4

3

3

2

2

1

1,k k k k k z

4

4

3

3

2

2

1

1

.... z

k

v z

k

v z

k

v z

k

v

k

vz

z

+++=

4321 z z z z z

k z =

Generall k > k

4321 k k k k



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Worked Example 1:

A stratified soil consists approximately of alternating layers of sand & silt. The

sand layers are generally 150 mm in thickness and have a permeability of k = 6.5 x 10 1

mm/s, the silt layers are 1.80 m thick and have a k = 2.5 x 10 4 mm/s. Assuming thatwithin each layer flow conditions are isotropic, determine the ratio of the horizontal

permeability to that of the vertical.Solution:

Then,

mm z

smmk

150

/105.6

41

11

=

=

Horizontal permeability

mm z 1800

.

2

2

=

=

4

21

2211 101800150

)5.21800()6500150( +

+=

+

+=

z z

zk zk k H



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Vertical permeability

4

21

21 101800150

1800150 +

+=

+

+=

z z z z

k V

Therefore, ratio

.

186)180050.1(

..2

=+

++=

V

H

k



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gradient , ic of a granular soil in terms of the, s , .

What will be the value ofi

c whenG

s = 2.70an e = .



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lecture 6 flow of water part2 stratifiedsoil

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