Post on 04-Feb-2016
description
Seepage Analysis
Dr. Sayed Mohamed Elaraby
Ain Shams University
Faculty of Engineering
Structural Engineering Dept.
Geotechnical Group
3rd Year Civil
1
Table of Contents
Laplace Equation
Graphical Solution (Flow Nets)
Anisotropic Soils
Seepage Force
Check Heave
Check Piping
Filter Design
Earth Dams Phreatic Line in Earth Dams
Analytical Determination of the Phreatic Line and the Discharge
Flow Net for Earth Dams
2
Textbook: Braja M. Das, "Principles of Geotechnical Engineering", 7th Ed.
Laplace (Continuity) Equation
3
If the soil is isotropic
Solutions to Laplace's Equation
Computer solutions using finite element or
finite difference techniques.
Graphical solutions known as flow nets.
Flow Nets
4
Flow Lines and Equipotential Lines
A flow line is the path a water particle would follow in moving
from upstream to downstream.
An equipotential line is a line along which the total head is a
constant value.
Rules for Flow Net Construction in Isotropic Soils
Draw the situation to scale.
Establish the equipotential boundary conditions.
Establish the flow boundary conditions.
Flow lines and equipotential lines must always intersect at
right angles.
Fields are the spaces in a flow net formed by the intersecting
flow lines and equipotential lines. The fields should be
"square"
5
6
If piezometers were inserted into the ground with their tips on a single
equipotential then the water would rise to the same level in each standpipe
nd= 10
Dh= H/nd = H/10
Datum H 0
0.9H
0.8H
0.7H
0.1H
0.2H
0.3H
0.6H
0.5H
0.4H
nh= 4
No. of head drops
No. of flow channels
7
H 0 nd= 10
Dh= H/nd = H/10
nf= 4
No. of head drops
No. of flow channels
Flow channel
L
L
DQ Dq = K i L 1 = K (DH/L) . L = K . DH
Dq = K . H / nd
Q = Dq . nf = K H (nf / nd)
Shape factor = (nf / nd)
8
Example
= 6m = 9m
= 3m
40m
2m
40m
4.6
7
3.6
7
4.3
3
3.0
0
1m
2.3
3
1.6
7
1.0
0
-5.0
0
-4.0
0
-5.0
0
ht
z
Pressure head (u/gw)= total head - position head
= 10-5 m/sec
q = K H (nf/nd)
q = 10-5 x 6 x (5/9)
= 3.33x 10-5 m3/sec/m
= 2.88 m3/day/m
Pressure head (u/gw)
9.6
7
5.0
0
4.0
0
4.0
0
Anistropic Soils
9
Transformations
10
Seepage force
11 11
H 0
Net seepage force = (P1-P2) L
L
L
P1= gw (h+Dh)
P2= gw h
= gw . Dh . L
Net seepage force per volume = (gw . Dh . L ) / L2
Net seepage force per volume = gw . i
g’s . Volume
gw . i. Volume
H 0
12
Check Heave
13
Example
Datum
gw = 62.4 lb/ft3
nd = 6 Dh = 25/6 = 4.167 ft
25 0
20.833
16.667 12.5 8.33
4.167
7
12.5
iav = [0.5 ( 12.5+7) – 0] / 20 = 0.488
FOS = [(112-62.4) / 62.4] / 0.488 = 1.62
14
Check Piping
15
exitexit L
hi
Dexit
critical
i
iFOS
wcriticali g
g '
Lexit
Lexit
Filter design
16
Uncontrolled seepage accounts for approximately 50% of all dam failures in USA.
Erosion piping (aka., suffusion / suffosion: fines are washed away by seepage) may be responsible for up to 30% of all piping failures.
Filter allows drainage without suffusion.
17
18
Retention criteria:
D15, F < 4 to 5 D85, s
Permeability criteria:
D15, F > 4 to 5 D15, S
The size of the voids in the filter material should be small enough to
hold the larger particles of the protected material in place.
The filter material should have a high hydraulic conductivity to
prevent buildup of large seepage forces and hydrostatic pressures in
the filters.
Diameter (mm)
Pa
ssin
g (
%)
A
5A B 5B
19
Diameter (mm)
Pa
ssin
g (
%)
A
5A B 5B
Additional Filter requirements:
Fines % < 5 %
Maximum grain size = 75 mm
U ifor ity coefficie t ≤ 3
Phreatic Line in Earth Dams
20
m
0.3m
Focus
The phreatic line is the groundwater
surface with the pressure head = 0
The total head = the position head
Phreatic line is a flow line
21 2 3 1
22
23
a
Da
b
Da + a Da
Da + a
Da
24
Casagrade 1st graphical approximation b < 30
25
Casagrade 2nd graphical approximation b < 60
(it remains a good approximation to b < 90)
26
b b b b b b b b
Analytical Determination of the Phreatic
Line and the Discharge
27
28
Flow Net for Earth Dams
29
30
Questions ?