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
4/2/2013DR. BAKENAZ ZEDAN
7. CASE 1 : RESERVOIR IS EMPTY
(JUST AFTER CONSTRUCTION)
DR. BAKENAZ ZEDAN 4/2/2013
WWeight 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
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h
P
Wwd
W
N.D.W.L.
8
9. CASE 3 : RESERVOIR IS FULL
FLOOD DISCHARGE CONDITIONS
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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
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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
4/2/2013DR. BAKENAZ ZEDAN
h
hd
UU= 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
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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
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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
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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
4/2/2013DR. 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.
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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
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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.
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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:
4/2/2013DR. 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
4/2/2013DR. 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
4/2/2013DR. BAKENAZ
ZEDAN
1.Weight of
the dam
2. Thrust of
the tail
water
Force
sthat
give
stability 1. Reservoir
water
pressure
2. Uplift
3. Ice pressure
4. Temperature
stresses
6. Silt pressure
Static
Force
sthat try to
destabiliz
e
26
27. ACTING DYNAMIC FORCES
4/2/2013DR. BAKENAZ
ZEDAN
1.Weight of
the dam
2. Thrust of
the tail
water
Force
sthat
give
stability 1.Seismic
forces
2.Hydrodynami
c pressure
3.Forces due
to waves in the
reservoir
4. Wind
pressure
Dynami
c
Forcesthat try
todestabiliz
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
4/2/2013DR. 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.
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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.
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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
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
4/2/2013DR. 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
4/2/2013DR. 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:
4/2/2013DR. 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 certainrange of
DR. BAKENAZ ZEDAN
4/2/2013
43
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°)
