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)

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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


hP

Wwd

W

N.D.W.L.

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CASE 3 : RESERVOIR IS FULLFLOOD DISCHARGE CONDITIONS


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


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


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



Hydrodynamic pressure

Hydrostatic pressure N.U.W.L.

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CASE 6 = FLOOD DISCHARGE CONDITIONS + EARTHQUAKE FORCES


h'

H’d

γw

h’d

P’= γw

h’ δ

W’w

P’ W’wd

P’d

Ws

WV

Ps

P’hyd H


Hydrostatic pressure F.U.W.L.



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


Hydrostatic pressure N.U.W.L.



CASE 8 = FLOOD DISCHARGE CONDITIONS + EARTHQUAKE FORCES+ EXTREME UPLIFT


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


Hydrostatic pressure F.U.W.L.



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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.


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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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.


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


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.


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.


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


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 OVERTURNING

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SAFETY AGAINST OVERTURNING

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B

Mr

Mo

Heel toe

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SAFETY AGAINST FORWARD SLIDING

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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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Heel toeDam bse

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THE FACTOR OF SAFETY AGAINST SLIDING AND SHEAR:

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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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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


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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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°)

QUESTIONS

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