This document discusses the analysis of safety and stability for concrete gravity dams. It begins with an outline of the topics to be covered in Lecture 5, including a summary of loading cases, design of concrete gravity dams, safety analysis, and stability analysis. The document then provides detailed descriptions and diagrams for each of the 8 loading cases to be considered in the safety and stability analysis. It discusses the design of gravity dams and the procedures for analysis. Key aspects of the safety and stability analysis are described, including checking for overturning, sliding, shear stresses, and overstressing of the concrete. Diagrams are provided to illustrate the concepts of checking for overturning, sliding, and factors of safety.

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

2. GRAVITY DAMS LECTURES TOPICS
1. CLASSIFICATION & COMPONENTS
2. PLANNING & STRUCTURAL DESIGN
3. SEISMIC FORCES & CASES OF LOADING
4. SAFETY & STABILITYANALYSIS
5. STRESS ANALYSIS & DESIGN CRITERIA
6. CONSTRUCTION & FOUNDATION TREATMENT
2
4/2/2013
DR. BAKENAZ
ZEDAN

3. GRAVITY DAMS LECTURES TOPICS
1. CLASSIFICATION & COMPONENTS
2. PLANNING & STRUCTURAL DESIGN
3. SEISMIC FORCES & CASES OF LOADING
4. SAFETY & STABILITYANALYSIS
5. STRESS ANALYSIS & DESIGN CRITERIA
6. CONSTRUCTION & FOUNDATION TREATMENT
3
4/2/2013
DR. BAKENAZ
ZEDAN

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

5. DR.BAKENAZZEDAN 4/2/2013

6. SUMMING UP CASES OF LOADING
Case 1: Reservoir is Empty - Just After 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
4/2/2013
DR. BAKENAZ ZEDAN

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

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

9. CASE 3 : RESERVOIR IS FULL
FLOOD DISCHARGE CONDITIONS
4/2/2013
DR. BAKENAZ ZEDAN
h'
h’d
U
’
U’= γw
h’
γw
h’d
P’= γw
h’
δ
W’w
P’ W’wd
F
.D.W.L
P’d
Ws
W
Ps
Hydrostatic pressure
F
.U.W.L.
9

10. CASE 4 = RESERVOIR IS EMPTY + SEISMIC FORCES
4/2/2013
DR. BAKENAZ ZEDAN
W
V
H
Horizontal inertia forces due to
earthquake accelerations
Vertical inertia forces due to
earthquake accelerations
Weight of the dam
10

11. CASE 5 = NORMAL OPERATING CONDITIONS +
EARTHQUAKE FORCES
4/2/2013
DR. BAKENAZ ZEDAN
h
hd
U
U= γw
h
γw
hd
P= γw
h δ
Ww
P Wwd
Pd
Ws
W
V
Ps
Phyd H
P=Cs .γw .α.h
Vertical inertia forces due to
earthquake accelerations
Horizontal inertia forces due to
earthquake accelerations
Hydrodynamic pressure
Hydrostatic pressure
N.U.W.L.
11

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

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

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

15. DESIGN OF GRAVITY DAMS
15
DR. BAKENAZ ZEDAN 4/2/2013
 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.

16. DESIGN OF GRAVITY DAMS
 Technically, 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
4/2/2013
DR. BAKENAZ ZEDAN

17. DESIGN OF GRAVITY DAMS
17
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 to
prevent sliding.
These types of dams are susceptible to settlement,
overturning, sliding and severe earthquake shocks.
4/2/2013
DR. BAKENAZ ZEDAN

18. PROCEDURE OF CONCRETE GRAVITY DESIGN
18
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
4/2/2013
DR. BAKENAZ ZEDAN

19. STABILITY CRITERIA
19
Stability analyses are performed for various
loading conditions
The structure must prove its safety and
stability
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) versus Ice load
(winter). then no need to consider these
two forces at the same time.
DR. BAKENAZ ZEDAN 4/2/2013

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

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

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

23. STABILITY ANALYSIS OF GRAVITY DAMS
23
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
DR. BAKENAZ ZEDAN 4/2/2013

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

25. CLASSIFICATION OF LOADING 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.
25
4/2/2013
DR. BAKENAZ
ZEDAN
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.
Normal Loads Abnormal Loads
Water pressure corresponding to
full reservoir level.
Higher water pressure during floods
Weight of dam and structure above it. Earthquake force
Uplift. Silt pressure
Wave pressure
Ice thrust
Thermal stresses

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

27. ACTING DYNAMIC FORCES
4/2/2013
DR. BAKENAZ
ZEDAN
1.Weight of
the dam
2. Thrust of
the tail
water
Force
s
that
give
stability 1.Seismic
forces
2.Hydrodynami
c pressure
3.Forces due
to waves in the
reservoir
4. Wind
pressure
Dynami
c
Forces
that try
to
destabiliz
e
27

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

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

30. STRUCTURAL STABILITY ANALYSIS
The stability analysis of a dam section
under
static and dynamic loads is carried out to
check the safety with regards to:
30
1. Rotation and overturning
Translation and sliding
Overstress and material
failure
2.
3.
4/2/2013
DR. BAKENAZ
ZEDAN

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

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

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

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

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

36. 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 wedge,
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
DR. BAKENAZ ZEDAN
4/2/2013
36

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

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

39. 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 of
concrete.
 Hence the strength in dam concrete should be
more than the anticipated in the structure by a safe
margin
 The maximum compressive stresses occur at:
at heel (at reservoir empty condition)
or at toe (at reservoir full condition)
and on planes normal to the face of the dam. 39
4/2/2013
DR. BAKENAZ
ZEDAN

40. 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
4/2/2013
DR. BAKENAZ
ZEDAN

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

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

43. 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
a certain
range of
DR. BAKENAZ ZEDAN
4/2/2013
43

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

45. DR. BAKENAZ
ZEDAN
STABILITY CRITERIA
The contact stress between the foundation and the dam or the internal
stress in the dam body must be compressive:
Tension along the upstream face of a gravity dam is possible under
reservoir operating conditions.
4/2/2013
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.BAKENAZZEDAN
46
4/2/2013
Given data:
Crest width 1 0 m
Base width 50m
Height of dam 60m
Height of reservoir 55m
Tail 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°)

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