This document discusses the safety and stability analysis of gravity dams. It covers the following key points in 3 sentences: Gravity dams derive stability from their weight resisting overturning forces from reservoir water. Various loading cases are analyzed including empty, full, seismic, and flood conditions. Stability is checked against overturning, sliding, shear stresses and overstressing to ensure safety factors are not exceeded under different load combinations.

1. FACULTY OF ENGINEERING
TANTA UNIVERSITY
DAMS & RESERVOIRS ENGINEERING
4TH YEAR CIVIL/STRUCTURE 2012-2013
LECTURE 5
GRAVITY DAMS
SAFETY & STABILITY
Instructor:
Dr. Bakenaz A. Zedan
ANALYSIS

2. DR. BAKENAZ
ZEDAN
4/2/2013
GRAVITY DAMS LECTURES TOPICS
CLASSIFICATION &
COMPONENTS
PLANNING & STRUCTURAL
DESIGN
SEISMIC FORCES & CASES OF
LOADING
SAFETY & STABILITYANAL
YSIS
1.
2.
3.
4.
STRESSANAL
YSIS & DESIGN
CRITERIA
5.
CONSTRUCTI
ON
& FOUNDATION
TREATMENT
6.
2

3. DR. BAKENAZ
ZEDAN
4/2/2013
GRAVITY DAMS LECTURES TOPICS
CLASSIFICATION &
COMPONENTS
PLANNING & STRUCTURAL
DESIGN
SEISMIC FORCES & CASES OF
LOADING
SAFETY & STABILITYANAL
YSIS
1.
2.
3.
4.
STRESSANAL
YSIS & DESIGN
CRITERIA
5.
CONSTRUCTI
ON
& FOUNDATION
TREATMENT
6.
3

4. DR. BAKENAZ
ZEDAN
4/2/2013
LECTURE 5
 Summary
Of
OUTLINE:
Cases Of
Loading
 Design Of Concrete Gravity
Dams
 Safety Of Concrete Gravity
Dams
 Stability Analysis
Stability
Against
Stability
Against
Stability
Against
Stability
Against
Forward Overturning
Forward Sliding
Sliding
& Shear Concrete
Overstresses
Foundation
Overstresses
1.
2.
3.
4.
5.
 Solved
Example 4

5. DR.BAKENAZZEDA
N
4/2/201
3

6. SUMMING UP CASES OF LOADING
Case 1: Reservoir is Empty - JustAfter Construction
Case 2: Reservoir is Full - Normal Operating
Conditions Case 3: Reservoir is Full - Flood Discharge
Conditions Case 4: Reservoir is Empty + Seismic
Forces
Case 5: Normal Operating Conditions + Seismic Forces
Case 6: Flood Discharge Conditions + Seismic Forces
Case 7: Normal Operating Conditions + Seismic Forces +
Extreme Uplift
Case 8: Flood Discharge Conditions + Seismic
Forces+ Extreme Uplift
6

7. DR. BAKENAZ ZEDAN 4/2/2013
CASE 1 : RESERVOIR IS EMPTY
(JUST AFTER CONSTRUCTION)
Weight of the dam
W
7

8. DR. BAKENAZ ZEDAN 4/2/2013
CASE 2
NORMAL
: RESERVOIR IS FULL
OPERATING CONDITIONS
Hydrostatic pressure
N.U.W.L.
W
Wwd
P Ws N.D.W.L.
Pd
U hd
γw
hd
s
P= γw
h
δ
U= γw
h
8
W
h
P
P
w

9. CASE 3 : RESERVOIR IS FULL
FLOOD DISCHARGE CONDITIONS
F
.U.W.L.
W
W’wd
Ws F
.D.W.L
P’d
U
’
h’d
γ
s
P’=
h’
γ
δ
w w
h’d
U’=
h’
γw
9
Hydrostatic pressure W
h'
P’
P
’w

10. CASE 4 = RESERVOIR IS EMPTY + SEISMIC FORCES
Vertical inertia forces due to
earthquake accelerations Horizontal inertia forces due to
earthquake accelerations
V
H
Weight of the dam
W
10

11. Pd
CASE 5 = NORMAL OPERATING CONDITIONS +
EARTHQUAKE FORCES
Hydrodynamic pressure
Hydrostatic pressure Vertical inertia forces due to
earthquake accelerations
N.U.W.L.
W
V
Horizontal inertia forces due to
earthquake accelerations
H Wwd
Ws
P= γw
h
γw
hd
P=Cs .γw .α.h
δ
U= γw
h
U
hd
Phyd
W
P h
w
Ps

12. P d
DR. BAKENAZ ZEDAN 4/2/2013
CASE 6 = FLOOD DISCHARGE CONDITIONS +
EARTHQUAKE FORCES
Hydrodynamic pressure
Hydrostatic pressure Vertical inertia forces due to
earthquake accelerations
F
.U.W.L.
W
V
Horizontal inertia forces due to
earthquake accelerations
H W’wd
Ws
s
d
P’= γw
h’
P’=Cs .γw .α.h’
γw
h’d
δ
U’=
h’
γw
U
’ 12
H’ ’
P’hyd
W
P’ h'
’w
P

13. Pd
DR. BAKENAZ ZEDAN 4/2/2013
CASE 7 = NORMAL OPERATING CONDITIONS +
EARTHQUAKE FORCES + EXTREME UPLIFT
Hydrodynamic pressure
Hydrostatic pressure Vertical inertia forces due to
earthquake accelerations
N.U.W.L.
W
V
Horizontal inertia forces due to
earthquake accelerations
H Wwd
Ws
P= γw
h
γw
hd
P=Cs .γw .α.h
U= γw
h
U 13
hd
Phyd
W
P h
w
Ps

14. P d
DR. BAKENAZ ZEDAN 4/2/2013
CASE 8 = FLOOD DISCHARGE CONDITIONS +
EARTHQUAKE FORCES+ EXTREME UPLIFT
Hydrodynamic pressure
Hydrostatic pressure Vertical inertia forces due to
earthquake accelerations
F
.U.W.L.
W
V
Horizontal inertia forces due to
earthquake accelerations
H W’wd
Ws
U d
’
P’= γw
h’
γw
h’d
U’= γw
h’
P’=Cs .γw .α.h’
14
H’ ’
P’hyd
W
P’ h'
’w
Ps

15. DR. BAKENAZ ZEDAN 4/2/2013
DESIGN OF GRAVITY DAMS
INTRODUCTION:
Dams are national properties, for the
development of national economy in which large
investments are deployed
Safety of dams is a very important aspect for
safeguarding national investmentand
benefits derived by the project
Unsafe dams constitute hazards to human life
in the downstream reaches
Safety of dams and allied structures is an
important aspect to be examined to ensure
public confidence and to protect downstream
area from any potential hazards.
15






16. DR. BAKENAZ ZEDAN 4/2/2013
DESIGN OF GRAVITY DAMS
 T
echnically, a concrete gravity dam derives its
stability from the force of gravity of its materials.
 The gravity dam has sufficient weight so as to
withstand the force and the over turning
moments caused by the water impounded in
the reservoir behind it.
 It transfers the loads to the foundations by
cantilever action and hence good foundations
ar
e pre requisite for the gravity dam.
16

17. DR. BAKENAZ ZEDAN 4/2/2013
DESIGN OF GRAVITY DAMS
Gravity dams are satisfactorily adopted for narrow valleys
having
stiff geological formations.
Their own weight resists the forces exerted upon them.
They must have sufficient weight against overturning
tendency about the toe.
The base width of gravity dams must be large enough
prevent sliding.
These types of dams are susceptible to settlement,
overturning, sliding and severe earthquake shocks.
to
17

18. DR. BAKENAZ ZEDAN 4/2/2013
PROCEDURE OF CONCRETE GRAVITY DESIGN
In the gravity dam calculations one should proceed through the following
steps:
1determination of all expected acting loads
2 state the combination of acting loads for each case of loading
3check stability against overturning for all possible cases of loading (cases
of full reservoir)
4 check stability against forward sliding for all possible cases of loading
(cases
of full reservoir)
5determine normal stress distribution at dam base and any given sections
for all cases of loading
6determine maximum and minimum principal and shear stresses at
dam base and any given sections for all cases of loading
7compare results with corresponding factors of safety and allowable
stresses 8- approve the dam profile or redesign for a new profile
18

19. DR. BAKENAZ ZEDAN 4/2/2013
STABILITY CRITERIA
analyses are performed for various
loading conditions
Stability
The structure
stability
must prove its safety and
under all loading conditions.
Since the probability of occurrence of extreme events is
relatively small, the joint probability of the independent
extreme events is negligible. In other words, the
probability that two extreme events occur at the
same time is relatively very low.
Therefore, combination of extreme events are
not considered in the stability criteria.
e.g. Floods (spring and summer)
need to
versus Ice load
(winter). then no
at the
consider these
two forces same time. 19

20. DR. BAKENAZ ZEDAN 4/2/2013
STABILITY CRITERIA
Usual Loading
Hydrostatic force (normal operating
level) Uplift force
T
emperature stress
Dead
loads Ice
loads Silt
load
(normal temperature)
Unusual Loading Hydrostatic
force (reservoir full) Uplift
force
Stress produced by minimum
level Dead loads
Silt load
Extreme (severe) Loading
temperature at full
20

21. DR. BAKENAZ ZEDAN 4/2/2013
STABILITY CRITERIA
The ability of a dam to resist the applied loads
measured by some safety factors.
T
o offset the uncertainties in the loads, safety
is
criteria are chosen sufficiently
equilibrium condition.
Recommended safety factors:
1987)
However, since each dam site
beyond the static
(USBR, 1976 and
has unique features,
different safety Factors may be derived considering
the local condition.
21

22. DR. BAKENAZ ZEDAN 4/2/2013
STABILITY CRITERIA
F
.S0: Safety factor against overturning.
F
.Ss: Safety factor against sliding.
F
.Sss: Safety factor against shear and sliding.
22

23. DR. BAKENAZ ZEDAN 4/2/2013
STABILITY ANAL
YSIS OF GRAVITY DAMS
1 Stability against overturning
2 Stability against Forward sliding
3 Failure against overstressing
Normal stresses on horizontal
planes Shear stresses on
horizontal planes
Normal stresses on vertical planes
Principal stresses
Permissible stresses in concrete 23

24. DR. BAKENAZ
ZEDAN
4/2/2013
STABILITY ANAL
YSIS OF CONCRETE GRAVITY DAMS
 For the considerations of stability of a concrete
gravity dam the following assumptions are made:
• Is composed of individual transverse vertical
elements each of which carries
foundation separately
its load to the
the
dam
• Is carried out for the whole
block
Stabilit
y
analysi
s
vertica
stress
• Varies linearly from upstream face to downstream
face on any horizontal section
l
24

25. DR. BAKENAZ
ZEDAN
4/2/2013
CLASSIFICA
TION OFLOADING FOR DESIGN
Normal Loads
They are those, under the combined action of which the dam shall have adequate
stability
, and the factors of safety and permissible stresses in the dam shall not be exceeded.
Abnormal Loads
These are the loads which in combination with normal loads encroach upon the factor of
safety and increase the allowable stresses although remaining lower than the higher emergency
stress limits.
25
Normal Loads Abnormal Loads
Water pressure corresponding to Higher water pressure during floods
full reservoir level.
Weight of dam and structure above it. Earthquake force
Uplift. Silt pressure
Wave pressure
Ice thrust
Thermal stresses

26. DR. BAKENAZ
ZEDAN
4/2/2013
ACTING STATIC FORCES
Static
Force
th
sat
Force
ths
at try to
give destabiliz
e
stability
water
26
1. Reservoir
pressure
2. Uplift
3. Ice pressure
4. T
emperature
stresses
6. Silt pressure
1.Weight of
the dam
2. Thrust of
the tail
water

27. DR. BAKENAZ
ZEDAN
4/2/2013
ACTING DYNAMIC FORCES
Dynami
Force
th
sat
c
th
Faotrtcre
ys
give d
to
estabiliz
e
stability
2.Hydrodynami
water
pressure
27
1.Seismic
forces
c pressure
3.Forces due
to waves in the
reservoir
4. Wind
1.Weight of
the dam
2. Thrust of
the tail

28. DR. BAKENAZ
ZEDAN
4/2/2013
SAFETY OF
CONCRETE
Equilibrium states that:
GRAVIT
Y
DA
M
∑FX=0, ∑FY=0, ∑M@ any
point=0 Should attained
otherwise
If
If
If
If
∑FX ≠ 0, forward sliding may occur
∑FY ≠ 0, settlement may occur
∑M ≠ 0 forward overturning may occur
eccentricity exceeds B/6 , tension forces may
occur If working stresses
than allowable stresses
greater
failure may occur due to excessive stresses or 28

29. DR. BAKENAZ
ZEDAN
4/2/2013
SAFETY OF CONCRETE GRAVITY
Thus a dam profile should be safe against:
DAM
forward sliding and translation
Settlement or tilting
1.
2.
forward overturning
T
ensile stresses
failure due to over
stresses Cracks &
material failure
or rotation
3.
4.
5.
6.
7.
Higher responses than allowable
limit
according to codes 29

30. DR. BAKENAZ
ZEDAN
4/2/2013
STRUCTURAL STABILITY ANAL
YSIS
The stability analysis of a dam section
under
static and dynamic loads is carried out to
1.heck
2.
tR
he
ots
aa
tifo
en
tyaw
nd
ith
ov
re
eg
rt
a
u
rr
d
n
s
in
tg
o:
Translation
Overstress
failure
and
and
sliding
material
3.
30

31. DR. BAKENAZ
ZEDAN
4/2/2013
SAFETY AGAINST OVERTURNING

31

32. DR. BAKENAZ
ZEDAN
4/2/2013
SAFETY AGAINST OVERTURNING
Mo
toe
Heel
B
Mr
32

33. DR. BAKENAZ
ZEDAN
4/2/2013
SAFETY AGAINST FORWARD SLIDING

33

34. DR. BAKENAZ
ZEDAN
4/2/2013
SAFETY AGAINST FORWARD SLIDING
34

35. DR. BAKENAZ
ZEDAN
4/2/2013
SAFETY AGAINST FORWARD SLIDING

35

36. e,
DR. BAKENAZ ZEDAN
4/2/2013
SAFETY AGAINST FORWARD SLIDING
In the presence of a horizon with low
shear resistance the net shear force
may equal to:
(W cosα+ ∑Hsin α) tanφ
where W is the passive resistance wedg
α is the assumed angle of sliding failure,
∑H is the net de-stabilizing horizontal moment,
and φ is the internal friction within the rock at plane
B-B
36

37. DR. BAKENAZ
ZEDAN
4/2/2013
SAFETY AGAINST FORWARD SLIDING
toe
Heel Dam bse
37

38. DR. BAKENAZ ZEDAN
4/2/2013
THE FACTOR OF SAFETY AGAINST SLIDING AND SHEAR:

38

39. DR. BAKENAZ
ZEDAN
4/2/2013
SAFETY AGAINST OVERSTRESSING
 A dam may fail if any of its part is overstressed
and hence the stresses at any part of the dam
should not exceed the allowable working stress
concrete.
 Hence the strength in dam concrete should be
of
more than the anticipated in the structure by a
margin
 The maximum compressive stresses occur at:
safe
at heel (at reservoir empty condition)
or
and
at toe (at reservoir full condition)
on planes normal to the face of the dam. 39

40. DR. BAKENAZ
ZEDAN
4/2/2013
SAFETY AGAINST OVERSTRESSING
For design considerations, the calculation of
the stresses in the body of the dam follows
from the basics of elastic theory, which is
applied in two- dimensional vertical plane, and
assuming the block of the dam to be a
cantilever in the vertical plane attached to the
foundation.
The contact stress between the foundation
and the dam or the internal stress in the dam
body must be compressive. 40

41. DR. BAKENAZ ZEDAN
4/2/2013
SAFETY AGAINST CONCRETE OVERSTRESSING
∑V
B
σtoe
flexural stres σheel
Normal stress Bending or
s
Base pressure distribution
41

42. DR. BAKENAZ
ZEDAN
4/2/2013
NORMAL
Normal stress:
STRESSES AT DAM BASE
∑V
y
∑H
c.g.
Heel toe
e
B
My
1m
+ x
σnheel
σntoe
42

43. DR. BAKENAZ ZEDAN
4/2/2013
SAFETY AGAINST FOUNDATION OVERSTRESSING
AT DAM BASE
Naturally, there would be tension on the upstream face
if the overturning moments under the reservoir full
condition increase such that e becomes greater than
B/6. The total vertical stresses at the upstream and
downstream faces are obtained by addition of external
hydrostatic pressures.
The contact stress between the foundation and the
dam or the internal stress in the dam body must be
compressive. In order to maintain compressive
stresses in the dam or at the foundation level, the
minimum pressureσmin ≥0. This can be achieved with
rac
ne
gr
e
ta
o
in
f 43

44. DR. BAKENAZ ZEDAN
4/2/2013
OVERSTRESSING
SAFETY AGAINST
e
σheel
σtoe
Base pressure distribution
44
For
a
unit
width

45. DR. BAKENAZ
ZEDAN
STABILITY CRITERIA
4/2/2013
The contact stress between the foundation and the dam or the internal
stress in the dam body must be compressive:
T
ension along the upstream face of a gravity dam is possible under
operating conditions.
reservoir
z = 1.0 (if there is no drainage in the dam body)
z = 0.4 (if drains are used)
P: hydrostatic pressure at the level under consideration
45

46. DR.BAKENAZZEDA
N
4/2/201
3
Given data:
Crest width 1 0 m
Base width 50mHeight
of dam 60mHeight of
reservoir 55mTail water
height 0 m
Height of sedimentation 10m
Unit weight of concrete =24 KN/m3
Modulus of Elasticity= 28 MPa
Unit weight of water= 10 KN/m3
Unit weight of sedimentation =14 KN/m3
Seismic coefficient= 0.2
Required:
Check the stability of the dam profile
( q>= 30°)
46

47. DR. BAKENAZ
ZEDAN
4/2/2013
QUESTIONS
47