7 permeability zu
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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
. .
.
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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
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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
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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
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Permeability of stratified soils
+ water =
Compactive
effort
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+ 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.
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+ 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 +
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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:
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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
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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
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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
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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.
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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.
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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.
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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 !(
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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
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f
d N
NHkqand
N
Hkq
..,
.!!(
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Cofferdam
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Protective Filters
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Protective Filters
D15 Filter > 4D15 Soil
D15 Filter < 4D85
Soil
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Protective Filters
D15 Filter > 4D15 Soil
D15 Filter < 4D85
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