Transcript permeability

Seepage Through Porous Media
W.T.
Impervious Soil
)h = hA - hB
W.T.
hA = total head
Impervious Soil
Datum
hB= total head
W.T.
Impervious Soil
)h = hA - hB
W.T.
hA
Water In
Impervious Soil
Datum
hB
q = v . A = k i A = k DhA
L
Head Loss or
Head Difference
or Energy Loss
)h =hA - hB
i = Hydraulic Gradient
hA
(q)
Water
out
hB
ZA
ZB
Datum
Bernouli’s Equation:
Total Energy = Elevation Energy + Pressure Energy + Velocity Energy
or
Total Head = Elevation Head + Pressure Head + Velocity Head
htotal =
Z
+
P
g
+
V2
2g
Darcy’s Law:
v%i
v=ki
v = discharge velocity & i = hydraulic gradient
k = coefficient of permeability
v = k )h/L
To determine the rate of flow, two parameters are needed
* k = coefficient of permeability
* i = hydraulic gradient
k can be determined using
1Laboratory Testing
2Field Testing
3Empirical Equations
i can be determined
1from the head loss
2flow net
[constant head test & falling head test]
[pumping from wells]
Seepage Through Porous Media
Water In
L = Drainage Path
Head Loss or
Head Difference
or Energy Loss
i = Hydraulic Gradient
)h =hA - hB
hA
Water
out
A
Porous
Stone
Soil
L
hB
Datum
B
Porous
Stone
Seepage Through Porous Media
Water In
L = Drainage Path
Head Loss or
Head Difference
or Energy Loss
i = Hydraulic Gradient
)h =hA - hB
hA
Water
out
A
ZA
Porous
Stone
Soil
hB
B
Porous
Stone
L
Datum
ZB
No Seepage
Piezometer
In
Flow
3 ft
D
u = 6 x 62.4
C
u = 14 x 62.4
14 ft
Out
Flow
2 ft
4 ft
B
W
s
12 ft
W
W
s
s
W
s
W
s
Buoyancy
8 ft
A
3 ft
3 ft
Datum
In
Flow
Piezometer
3 ft
u = 6 x 62.4 + Du
Du
17 ft
u = 17 x 62.4
Upward Seepage
D
C
Out
Flow
2 ft
4 ft
B
12 ft
W
s
W
W
s
8 ft
s
W
s
W
s
Buoyancy + Seepage Force
A
3 ft
3 ft
Datum
Downward Seepage
Piezometer
3 ft
u = 6 x 62.4 - Du
D
10 ft
u = 17 x 62.4
Out
Flow
In
Flow
2 ft
C
4 ft
B
12 ft
Seepage Force
8 ft
W
s
W
W
s
s
W
s
A
3 ft
W
s
Buoyancy - Seepage Force
3 ft
Datum
No Seepage
1
1
g1 =110 pcf
W.T.
3 ft
2
2
4 ft
3
3
-
=
6 ft
4
4
12 ft
5
5
Total Stress
Total Stress
Pore Water Pressure
Effective Stress
Pore Water
Pressure
Effective Stress
u1 =
s1 =
u2 =
s2 =
s3 =
u3 =
s3 =
s4 =
u4 =
s4 =
s5 =
u5 =
s5 =
s1 =
s2 =
W
s
W
W
s
s
W
s
W
s
Buoyancy
No Seepage
W.T.
1
g1 =110 pcf
3 ft
4 ft
2
-
6 ft
=
3
12 ft
4
Total Stress
Pore Water
Pressure
Effective Stress
W
s
W
W
s
s
W
s
W
s
Buoyancy
No Seepage
W.T.
1
3 ft
g1 =110 pcf
2
3 ft
4 ft
3
-
6 ft
=
4
12 ft
5
Total Stress
Pore Water
Pressure
Effective Stress
W
s
W
W
s
s
W
s
W
s
Buoyancy
Upward Seepage
1
5 ft
g1 =110 pcf
W.T.
3 ft
2
4 ft
3
-
=
6 ft
4
12 ft
54
4
Total Stress
Pore Water
Pressure
Effective Stress
W
s
W
Total Stress
Pore Water Pressure
Effective Stress
W
s
s
W
s
W
s
Buoyancy + Seepage Force
Downward Seepage
g1 =110 pcf
1
W.T.
3 ft
1
3 ft
4 ft
2
2
3
=
6 ft
3
12 ft
4
4
Total Stress
Total Stress
Pore Water Pressure
Pore Water
Pressure
Effective Stress
Seepage Force
Effective Stress
W
s
W
W
s
s
W
s
W
s
Buoyancy - Seepage Force
g1 =110 pcf
W.T.
3 ft
W.T.
3 ft
4 ft
4 ft
6 ft
6 ft
12 ft
12 ft
q = A k i = A k Dh
L
Equipotential
Lines
Flow Lines
Principles of the Flow Net
Equipotential Lines
Flow Element
Principles of the Flow Net
)h = head loss = one drop
Piezometer
1
2
3
4
5
Flow Element
Equipotential Lines
Total heads along this
line are the same
Datum
In
Flow
)h
)h
)h
)h
)h
)h
)h
)h
3 in
Out
Flow
2 in
8
Feff =
7
14 in
*(soil + * (water - ( - )h) * (water
6
u = [14 - (3. )h)].(water
5
4
Ws
3
Ws
Ws
2
1
Ws
Ws
2
Buoyancy + Seepage Force
Seepage Through Porous Media
IN
qx(in) = dz . dy kx (Mh/Mx)
qx(in) = dx . dz ky (Mh/My)
OUT
qx (out) = dz . dy kx (Mh/Mx + M2h/Mx2 dx
)
qx (out) = dx . dz ky (Mh/My + M2h/My2 dy
)
Equating q in and q out
Two sets of curves
Rate of Discharge = qout
Rate of Discharge = qin
Z
dy
X
Y
dZ
Rate of Discharge = qin
dx
Rate of Discharge = qout
Rate of Discharge = qin
(Rate of Discharge)in = (Rate of Discharge)out
Rate of Discharge = qin