The document discusses geotechnical engineering principles focusing on water flow through soils, including the determination of hydraulic conductivity (k) and hydraulic gradient (i) through laboratory and field tests. It elaborates on flow nets, comprising flow lines and equipotential lines, and emphasizes their significance in analyzing seepage and fluid behavior in soil. The content is aimed at undergraduate civil engineering students and provides practical examples and rules for constructing flow nets.

1. 1
Geotechnical Engineering–I [CE-221]
BSc Civil Engineering – 4th Semester
by
Dr. Muhammad Irfan
Assistant Professor
Civil Engg. Dept. – UET Lahore
Email: mirfan1@msn.com
Lecture Handouts: https://groups.google.com/d/forum/2016session-geotech-i
Lecture # 27
3-May-2018

2. 2
WATER FLOW THROUGH SOILS
To determine the quantity of flow, two parameters are needed
* k = hydraulic conductivity
* i = hydraulic gradient
Determination of ‘k’
1- Laboratory Testing  [constant head test & falling head test]
2- Field Testing  [constant/falling head tests, pump out tests, etc]
3- Empirical Equations
Determination of ‘i’
1- From the head loss and geometry
2- Flow Nets
(how permeable is the soil medium)
(how large is the driving head)
Today’s
discussion
A
h
kAikq 


L

3. 3
FLOW NETS
A Flow Net consists of two groups of curves:
Flow lines: Flow lines (aka stream lines) represent the path that a particle of
water takes as it travels through the soil mass.
Equipotential lines: Equipotential lines are lines that pass through points of
equal head.
Equipotential lines
Flow lines
Total head
Head loss
Datum
x
y
z
h = 0.5h

4. 4
Flow lines
Total head
Head loss
FLOW NETS – Flow Lines
Flow lines: Flow lines (aka stream lines) represent the path that a
particle of water takes as it travels through the soil mass.
The space between two adjacent flow lines is called a flow path
Discharge through each flow path is equal.

5. 5
Equipotential lines
Total head
Head loss
Equipotential lines: Equipotential lines are lines that pass through points of equal
head.
The space between two adjacent equipotential lines represents a drop in head.
The space between two adjacent equipotential lines is called an equipotential space.
FLOW NETS – Equipotential Lines

6. 6
An equipotential line means potential head at all points is equal (i.e. total
head is constant).
Water in a piezometer (placed at different points along an equipotential line)
will rise to the same elevation.
Equipotential lines
Total head
Head loss
FLOW NETS – Equipotential Lines

7. 7
FLOW NET
k1 k1
k2 < k1
Total head

8. 8
DRAWING FLOW NETS
Equipotential lines
Flow Lines
Water IN
Head loss, Δh
1. Flow lines and equipotential lines are at right angles to one another.
2. Flow lines are ║ to no flow boundaries.
3. Equipotential lines are ║ to permeable boundaries.
4. Discharge through each flow path is equal.
5. Head loss through each equipotential space is equal.

9. 9
1. Flow lines and equipotential lines are at right angles to
one another.
2. Flow lines are ║ to no flow boundaries.
3. Equipotential lines are ║ to permeable boundaries.
DRAWING FLOW NETS
Asymmetric Flow
4. Discharge through each flow path is equal.
5. Head loss through each equipotential space is equal.

10. 10
Lines ab and cefd are the boundaries of this flow channel → Flow Lines
Line ca is the upstream equipotential boundary where the total head is h
Line bd is the downstream equipotential boundary where the total head is 0
h
h = h
h = 0
DRAWING FLOW NETS
Asymmetric Flow

11. 11
1. Draw Flow Channel Boundaries 2. Draw Equipotential Boundaries
Upstream
Equipotential Boundary
Downstream
Equipotential Boundary
DRAWING FLOW NETS
Seepage Around Obstruction

12. 12
DRAWING FLOW NETS
Seepage Around Obstruction
H
A
B

13. 13
DRAWING FLOW NETS
Seepage Around Obstruction

14. 14
DRAWING FLOW NETS
Seepage Around Obstruction

15. 15
RULES FOR DRAWING FLOW NETS
1) All impervious boundaries are flow lines.
2) All permeable boundaries are equipotentials.
3) All equipotentials are at right angles to flow lines.
4) All parts of the flow net must have the same geometric
proportions (e.g. square or similarly shaped rectangles).
5) Just like contour lines, flow lines cannot cross other flow lines
& equipotential lines cannot cross other equipotential lines.
6) Good approximations can be obtained with 4 - 6 flow channels.
More accurate results are possible with higher numbers of flow
channels, but the time taken goes up in proportion to the
number of channels.

16. 16
FLOW NETS UNDER DAM
Impounded
water
Tail water

17. 17
FLOW NET UNDER DAM WITH
TOE FILTER

18. 18
FLOW NET UNDER DAM WITH
SHEET PILE

19. 19
SEEPAGE AND FLOW NET
THROUGH DAM

20. 20
SEEPAGE ANALYSIS USING
SEEP/W
20 m
10 m
Kx= 1.0 e -005 m/sec
kx = ky
Head: 10 m
Head: 1 m
40 m
10 m 10 m20 m
21
22
23
24
25
26
27
28
29
30
3.3377e-005

21. 21
20 m
10 m
10 m 20 m 10 m
Head: 10 m
40 m
Head: 1 m
Kx = 1.0 e -005 m/sec
Kx = Ky
21
22
23
24
25
26
27
28
29
30
2.4766e-005
SEEPAGE ANALYSIS USING
SEEP/W

22. 22
SAMPLE FLOW NETS

23. 23
SAMPLE FLOW NETS

24. 24
SAMPLE FLOW NETS

25. 25
FLOW CALCULATIONS
Equipotential lines
Flow Lines
Water IN
Head loss, Δh
Flow Channel/Path
Potential/Equipotential Drop
dN
Hk
qchannelfloweachthroughFlow

,
k = permeability/hydraulic conductivity of soil
H = Head loss
Nd = Number of potential drops
f
d
N
N
Hk
flowTotal 


Nf = 1  for square channel
Nf = b/l  for rectangular channel

26. 26
FLOW CALCULATIONS
dN
Hk
qchannelfloweachthroughFlow

,
k = permeability/hydraulic conductivity of soil
H = Head loss
Nd = Number of potential drops
f
d
N
N
Hk
flowTotal 


Nf = 1  for square channel
Nf = b/l  for rectangular channel

27. 27
Practice Problem
f
d
N
N
Hk
flowTotal 


k = permeability of soil
H = Head loss
Nd = Number of potential drops
Nf = 1  for square channel
Nf = b/l  for rectangular channel

28. 28

29. 29
TOTAL HEAD DETERMINATION
USING FLOW NETS
h = 4.5-0.5 = 4.0m
3.33m
12
10
4.0hP 
Determination of total head
at any point, P
1. Downstream free water
surface is datum.
2. Show the total head, h
causing seepage.
3. Number the
equipotentials
4. At point P, the total
head is 10/12th of the
driving head

30. 30
CONCLUDED
REFERENCE MATERIAL
Principles of Geotechnical Engineering – (7th Edition)
Braja M. Das
Chapter #7 & 8