Download - 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
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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
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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
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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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.
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