LECTURE 5 safety and stability analysis- modified-2
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Transcript of LECTURE 5 safety and stability analysis- modified-2
FACULTY OF ENGINEERING TANTA UNIVERSITY
DAMS & RESERVOIRS ENGINEERING
4TH YEAR CIVIL/STRUCTURE 2012-2013
LECTURE 5GRAVITY DAMS
SAFETY & STABILITY ANALYSIS
Instructor:
Dr. Bakenaz A. Zedan
GRAVITY DAMS LECTURES TOPICS
1. CLASSIFICATION & COMPONENTS
2. PLANNING & STRUCTURAL DESIGN
3. SEISMIC FORCES & CASES OF LOADING
4. SAFETY & STABILITY ANALYSIS
5. STRESS ANALYSIS & DESIGN CRITERIA
6. CONSTRUCTION & FOUNDATION TREATMENT
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GRAVITY DAMS LECTURES TOPICS
1. CLASSIFICATION & COMPONENTS
2. PLANNING & STRUCTURAL DESIGN
3. SEISMIC FORCES & CASES OF LOADING
4. SAFETY & STABILITY ANALYSIS
5. STRESS ANALYSIS & DESIGN CRITERIA
6. CONSTRUCTION & FOUNDATION TREATMENT
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LECTURE 5 OUTLINE: Summary Of Cases Of Loading
Design Of Concrete Gravity Dams
Safety Of Concrete Gravity Dams
Stability Analysis
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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
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SUMMING UP CASES OF LOADINGCase 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
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CASE 1 : RESERVOIR IS EMPTY
(JUST AFTER CONSTRUCTION)
DR. BAKENAZ ZEDAN4/2/2013
WWeight of the dam
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hd
U
U= γw
h
γw
hd
P= γw
hδ
Pd
Ws
Ps
CASE 2 : RESERVOIR IS FULL
NORMAL OPERATING CONDITIONS
Hydrostatic pressure
N.U.W.L.
Ww
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hP
Wwd
W
N.D.W.L.
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CASE 3 : RESERVOIR IS FULLFLOOD DISCHARGE CONDITIONS
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h'
h’d
U’
U’= γw
h’
γw
h’dP’= γw
h’δ
W’w
P’ W’wd
F.D.W.L
P’d
Ws
W
Ps
Hydrostatic pressure
F.U.W.L.
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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
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CASE 5 = NORMAL OPERATING CONDITIONS + EARTHQUAKE FORCES
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h
hd
UU= γw
h
γw
hd
P= γw
h δ
Ww
P Wwd
Pd
Ws
WV
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.
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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
WV
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
CASE 7 = NORMAL OPERATING CONDITIONS + EARTHQUAKE FORCES + EXTREME UPLIFT
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h
hd
UU= γw
h
γw
hd
P= γw
h
Ww
P Wwd
Pd
Ws
WV
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
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
WV
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
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DESIGN OF GRAVITY DAMS
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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 investment and 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.
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 are pre requisite for the gravity dam.
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DESIGN OF GRAVITY DAMS
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Gravity dams are satisfactorily adopted for narrow valleys havingstiff 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 toprevent sliding.These types of dams are susceptible to settlement, overturning, sliding and severe earthquake shocks.
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PROCEDURE OF CONCRETE GRAVITY DESIGN
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In the gravity dam calculations one should proceed through the following steps:1determination of all expected acting loads2 state the combination of acting loads for each case of loading3check 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 (casesof full reservoir)5determine normal stress distribution at dam base and any given sections for all cases of loading6determine maximum and minimum principal and shear stresses at dam base and any given sections for all cases of loading7compare results with corresponding factors of safety and allowable stresses 8- approve the dam profile or redesign for a new profile
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STABILITY CRITERIA
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Stability analyses are performedfor various loading conditionsThe structure must prove its safety
and stabilityunder 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 extremeevents 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 thesame time.
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STABILITY CRITERIAUsual LoadingHydrostatic force (normal operating level) Uplift forceTemperature stress (normal temperature)Dead loads Ice loads Silt loadUnusual Loading Hydrostatic force (reservoir full) Uplift forceStress produced by minimum temperature at full level Dead loadsSilt loadExtreme (severe) LoadingForces in Usual Loading and earthquake forces
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STABILITY CRITERIA
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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 and1987)However, since each dam site has unique features, different safety Factors may be derived considering the local condition.
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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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STABILITY ANALYSIS OF GRAVITY DAMS
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1 Stability against overturning
2 Stability against Forward sliding
3 Failure against overstressingNormal stresses on horizontal planes Shear stresses on horizontal planesNormal stresses on vertical planesPrincipal stressesPermissible stresses in concrete
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STABILITY ANALYSIS OF CONCRETE GRAVITY DAMS
For the considerations of stability of a concrete gravity dam the following assumptions are made:
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thedam
• Is composed of individual transversevertical elements each of which carries its load to the foundation separately
Stability analysis
• Is carried out for the whole block
vertical stress
• Varies linearly from upstream face to downstream face on any horizontal section
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CLASSIFICATION OF LOADING FOR DESIGN
Normal LoadsThey are those, under the combined action of which the dam shall have adequatestability, and the factors of safety and permissible stresses in the dam shall not be exceeded.
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Abnormal LoadsThese 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
ACTING STATIC FORCES
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1.Weight of the dam2.Thrust
ofthe tail water
Forcesthat give stability
1.Reservoir water
pressure2.Uplift3. Ice pressure4.Temperaturestresses6. Silt pressure
StaticForces
that try to destabilize
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ACTING DYNAMIC FORCES
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1.Weight of the dam2.Thrust
ofthe tail water
Forcesthat give stability
1.Seismic forces
2.Hydrodynamic pressure3.Forces due to waves in the reservoir4.Wind
pressure
Dynamic
Forcesthat try todestabilize
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SAFETY OF CONCRETE GRAVITY DAM
Equilibrium states that:∑FX=0, ∑FY=0,∑M@ any
point=0 Should attained otherwiseIf ∑FX ≠ 0, forward sliding may occurIf ∑FY ≠ 0, settlement may occurIf ∑M ≠ 0 forward overturning may occur
If eccentricity exceeds B/6 , tension forcesmay occur If working
stresses greater than allowable stressesfailure may occur due to excessive stresses or crushing.
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SAFETY OF CONCRETE GRAVITY DAM
Thus a dam profile should be safe against:
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1.
forward sliding and translationSettlement or tiltingforward overturning or rotationTensile stressesfailure due to over stresses Cracks & material failureHigher responses than allowable limit
according to codes
2.3.4.5.6.7.
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STRUCTURAL STABILITY ANALYSIS
The stability analysis of a dam sectionunder
static and dynamic loads is carried out to check the safety with regards to:
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1.
Rotation and overturning Translation and sliding Overstress and material failure
2.3.
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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
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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.
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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.
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SAFETY AGAINST CONCRETE OVERSTRESSING
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Normal stress Bending or flexural stresσheel
s
σtoe
Base pressure distribution
∑V
B
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NORMAL STRESSES AT DAM BASE
Normal stress:
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c.g.
xMy
σnheel σntoe
1m +
∑V
y∑H
BHeel toe
e
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SAFETY AGAINST FOUNDATIONOVERSTRESSING
AT DAM BASENaturally, 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 pressure σmin ≥ 0. This can be achieved with a certainrange of eccentricity.
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SAFETY AGAINST OVERSTRESSING
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e
σheel
σtoe
Base pressure distributionFo
r a
un
it
wid
th
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DR. BAKENAZ ZEDAN
STABILITY CRITERIAThe 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.
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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
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DR.BAKENAZZEDAN
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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= 1 0 KN/m3
Unit weight of sedimentation =14
KN/m3 Seismic coefficient= 0.2
Required:
Check the stability of the dam profile
( q> = 30°)