1. ENV-2E1Y: Fluvial Geomorphology: 2004 - 5
Slope Stability and Geotechnics
Landslide Hazards
River Bank Stability
Section 2 - Water Flow in Soils
N.K. Tovey
Н.К.Тови М.А., д-р технических наук
Lecture 5
Lecture 6
Landslide on Main Highway at km 365 west of Sao Paulo: August 2002

2. pressure arising from a static head (wZ)
2.1 Introduction
Three component parts to the water pressure:-
pressure arising from a static head (wZ)
excess pore water pressure (pressure head differential which actually causes water flow. (u )
a velocity head =
total pore water pressure (pwp) =
total = position + pressure velocity
head head head head

3. 2.2 Hydraulic Gradient Standpipes P1 h1 h2 P2 Water In Water Out A B
Pressure at A is w h1
and at B is w h2
hydraulic gradient =
Standpipes P1 h1
more generally h2 P2
Water In
Water Out
NOTE: The hydraulic gradient as defined above is dimensionless (i.e. has no units).
some other disciplines A B
Soil Sample
.....(kNm-3)
Fig Flow of water in a simple channel section

4. 2.3 The Permeameter - (Constant Head)
Water IN
Q - flow rate
At - cross section area
Darcy’s Law h z

5. 2.5 Results from Permeameter
Loose Dense
e=0.744
k=5.89 mm/s
Quicksand occurs
Medium Dense
e=0.620
k=2.93 mm/s

6. 2.5 Results from Permeameter
m - total mass of sand
A - cross section of sand column
L - length (height) of column of sand
Volume occupied = A.L
Volume of Sand grains =

7. Further Comments about Permeability
Falling Head Permeameter is used for clays
- in constant head permeameter, flow rate is far to small to get meaningful readings
Formation of a Quicksand - Piping
occurs when upward seepage force
= downward force from self weight

8. Analogies in Heat Flow and Electricity
2.10 Flow of Water in Soils
Analogies in Heat Flow and Electricity
In HEAT FLOW - (ENV-2D02)
Where Q is the heat flow rate
1 is the internal temperature
2 is the external temperature
A is the cross-section area
k is the thermal conductivity
is the path length
In the FLOW of ELECTRICTY
Where I is the current
E1 is the inlet voltage
E2 is the outlet voltage
A is the cross-section area
k is the electrical conductivity
is the path length

9. 2.10 Flow of Water in Soils (continued)
In the FLOW of WATER in SOILS
Where Q is the water flow rate
h1 is the inlet head
h2 is the outlet head
A is the cross-section area
k is the permeability
is the path length
1) Mathematical solutions
a) exact solutions for certain simple situations
b) solutions by successive approximate e.g. relaxation methods
2) Graphical solutions
3) Solutions using the electrical analogue
4) Solutions using models
Only graphical methods will be used in this course

10. 2.12 Graphical Solutions - Flow Nets
Flow Lines
1) flow lines and equipotentials are at right angles to one another.
2) the cylinder walls are also flow lines.
3) distances between the equipotentials are equal
head drops between the equipotentials are also equal.
Equi-potentials
Water IN

11. 2.12 Asymetric Flow

12. 2.12 Asymetric Flow C A B Intersections are at right angles
approximate to curvilinear square D

13. 2.12 Asymetric Flow nd pressure drops C a A B
Intersections are at right angles
approximate to curvilinear square D

14. 2.12 Asymetric Flow (continued)
pressure drop between AB and CD is H
and let there be nd pressure drops and nf flow lines.
where qf is the flow per unit cross-section and
a x 1 is the cross- section between flow lines.
the total seepage =

15. Solutions are relatively straightforward.
Summary of Flow Nets
Solutions are relatively straightforward.
1) draw the appropriate flow net
2) count the number of pressure drops in the flow net
(over the relevant distance)
3) count the number of flow lines
4) do a simple calculation
work out total flow
work out pressure at any given point
etc.

16. 2.13 Seepage around an obstructionH A B

17. 2.13 Seepage around an obstruction
upward seepage force =
downward force of the soil =
A quicksand will occur if
actual downward force of the soil
Factor of safety =
downwards force required to resist seepage force
In the above example, nd = 10 and Nab ~ 3.5
but very approximately ' = w so
i.e. the distance must exceed 0.35 times the difference in head of water.

18. 2.14 Flow nets Summary Rules for drawing flow nets:- Water table
1) All impervious boundaries are flow lines.
2) All permeable boundaries are equipotentials
3) Phreatic surface - pressure is atmospheric, i.e. excess pressure is zero.
Change in head between adjacent equipotentials equals the vertical distance between the points on the phreatic surface.
4) All equipotentials are at right angles to flow lines
5) All parts of the flow net must have the same geometric proportions
(e.g. square or similarly shaped rectangles).
6) Good approximations can be obtained with 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.
The extra precision is usually not worth the extra effort.
Water table h h h h h h

19. 2.17 Uplift on Obstructions
Uplift arises the total water pressure exerted on the base.
Static head (constant for flat based obstruction)
excess head.
3 m
4 m
6 m 4 3 2 1
Head of Water (m)
Distance under obstruction (m) 2

20. 2.17 Uplift on Obstructions
If total uplift force > the self weight downward
object will be displaced downstream.
Draw flow net
Plot graph of uplift pressure (Y –axis) against distance along base (X-axis). Uplift pressure is estimate from flownet
head at the upstream head is ~0.75 of total head
head at the down stream end it is ~0.25 of the total head.

21. 2.17 Uplift on Obstructions
Base of the obstruction is 2m below the surface
uplift force from the static head is 2w multiplied by width
(i.e. 6w kN per metre length).
the upward force is the area under the curve multiplied by w.
In this example upward force = 6w kN per metre length,
i.e. in this case it equals the static head uplift.
total uplift = 12w kN m-1.
Uplift reduces ability of the obstruction to resist movement through the pressure of water
potential boulder blockages in a river
man-made drop structure built in river engineering works to dissipate energy (see RDH's part of the Course).
quicksand might form at the down stream end of the obstruction.

22. 2.3 The Permeameter - (Constant Head)
Water IN h z