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Datum
hA = total head
W.T.
h = hA - hB
W.T.
Impervious Soil
Impervious Soil
pervious Soil
hB= total head
Seepage Through Porous Media
A
BSoil
Water In
h =hA - hB
Head Loss orHead Difference or Energy Loss
hA
hB
i = Hydraulic Gradient
(q)Water
out
L = Drainage Path
Datum
hA
W.T.
hB
h = hA - hB
W.T.
Impervious Soil
Impervious Soil
ZA
Datum
ZB
Ele
v ati o
n H
e ad
Pre
s su r
e H
e ad
Pre
s su r
e H
e ad
Ele
v ati o
n H
e ad Tot
al H
ead
To
tal H
ea
d
q = v . A = k i A = k AhL
Bernouli’s Equation:
Total Energy = Elevation Energy + Pressure Energy + Velocity Energy
or
Total Head = Elevation Head + Pressure Head + Velocity Head
htotal = Z + P + V2
Darcy’s Law:
v i v = discharge velocity & i = hydraulic gradientv = k i k = coefficient of permeability
v = k h/L
Rate of Discharge = Q = v.A = k (h/L).A
2 g
To determine the rate of flow, two parameters are needed
* k = coefficient of permeability* i = hydraulic gradient
k can be determined using 1- Laboratory Testing [constant head test & falling head test]
2- Field Testing [pumping from wells]
3- Empirical Equations
i can be determined 1- from the head loss2- flow net
Water In
h =hA - hB
Head Loss orHead Difference or Energy Loss
hA
hB
A BDatum
PorousStone
PorousStone
Seepage Through Porous Media
i = Hydraulic Gradient
Soil
Waterout
L = Drainage Path
L
Water In
h =hA - hB
Head Loss orHead Difference or Energy Loss
ZA
hB
A B
Datum
PorousStone
PorousStone
Seepage Through Porous Media
i = Hydraulic Gradient
Soil
Waterout
L = Drainage Path
L
hA
ZB
14 ft
3 ft
12 ft
In Flow
Out Flow
2 ft
4 ft
Datum
3 ft
3 ft
8 ft
Piezometer
A
B
C
D
u =
6 x
62
.4
u =
14
x 6
2.4
No Seepage
Buoyancy
W
s
W
s
W
s
W
s
W
s
17 ft
3 ft
12 ft
In Flow
Out Flow
2 ft
4 ft
Datum
3 ft
3 ft
8 ft
Piezometer
A
B
C
D
u =
6 x
62
.4 +
u
u
u =
17
x 6
2.4
Upward Seepage
Buoyancy + Seepage Force
W
s
W
s
W
s
W
s
W
s
10 ft
3 ft
12 ft
In Flow
Out Flow
2 ft
4 ft
Datum
3 ft
3 ft
8 ft
Piezometer
A
B
C
D
u =
6 x
62
.4 -
u
u =
17
x 6
2.4
Downward Seepage
Buoyancy - Seepage Force
W
s
W
s
W
s
W
s
W
s
Seepage Force
3 ft
4 ft
6 ft
12 ft
=110 pcfW.T.
=
=
=
2
3
4
5
=
- =
Total Stress Pore WaterPressure
Total Stress Pore Water Pressure
2
3
4
5
No Seepage
Buoyancy
W
s
W
s
W
s
W
s
W
s
u =
u =
u =
u =
Effective Stress
=
=
=
=
1 1
= u = =
Effective Stress
3 ft
4 ft
6 ft
12 ft
=110 pcf
W.T.1
2
3
4
- =
Total Stress Pore WaterPressure
No Seepage
Buoyancy
W
s
W
s
W
s
W
s
W
s
Effective Stress
3 ft
4 ft
6 ft
12 ft
=110 pcf
W.T.
1
3
4
5
- =
Total Stress Pore WaterPressure
No Seepage
Buoyancy
W
s
W
s
W
s
W
s
W
s
3 ft
2
Effective Stress
3 ft
4 ft
6 ft
12 ft
W.T.
4
Total Stress Pore Water Pressure
Upward Seepage
Buoyancy + Seepage Force
W
s
W
s
W
s
W
s
W
s
=
Pore WaterPressure
5 ft =110 pcf
1
3
54
-
Total Stress
4
2
Effective Stress
Effective Stress
3 ft
4 ft
6 ft
12 ft
=110 pcfW.T.
1
2
3
4
- =
1
2
3
4
Total Stress Pore WaterPressure
Total Stress Pore Water Pressure
3 ft
Downward Seepage
Buoyancy - Seepage Force
W
s
W
s
W
s
W
s
W
s
Seepage ForceEffective Stress
Effective Stress
3 ft
4 ft
6 ft
12 ft
=110 pcfW.T. W.T. 3 ft
4 ft
6 ft
12 ft
q = A k i = A k hL
Flow Lines
EquipotentialLines
Flow Lines
Equipotential Lines
Flow Element
Flow Lines
Principles of the Flow Net
Flow LinesFlow Lines
Piezometer
h = head loss = one drop
Datum
To t
a l H
e ad
= E
lev a
t ion
h ea d
+ P
res s
u re
h ea d
Ele
v at io
n H
e ad
Pre
s su r
e H
e ad
1
2
3
4
5
Principles of the Flow Net
Equipotential LinesTotal heads along this line are the same
Flow Element
8
2
7
6
5
3
4
1
2
h
u = [14 - (3. h)].water
14 in
eff = *soil + * water - ( - h) * water
hhhhhhh
3 in
2 in
Buoyancy + Seepage Force
Ws
Ws
Ws
Ws
Ws
In Flow
Out Flow
Direction of Flow
Rate of Discharge = qin
XdZY
Seepage Through Porous Media
Rate of Discharge = qout
Rate of Discharge = qout
Rate of Discharge = qin
Rate of Discharge = qin
Rate of Discharge = qin
dy
dx
(Rate of Discharge)in = (Rate of Discharge)out
INqx(in) = dz . dy kx (h/x)qx(in) = dx . dz ky (h/y)
OUTqx (out) = dz . dy kx (h/x + 2h/x2 dx )qx (out) = dx . dz ky (h/y + 2h/y2 dy )
Equating q in and q out
Z
Two sets of curves
