chapter 6 concrete dam engineering with examples

CHAPTER 6: CONCRETE DAM

ENGINEERING

1

0401544 - HYDRAULIC STRUCTURES

University of Sharjah

Dept. of Civil and Env. Engg.

DR. MOHSIN SIDDIQUE

ASSISTANT PROFESSOR

LEARNING OUTCOME

After this lecture, students should be able to

(1). Learn about the dam, classification and types and understand the generalized criteria for dam site & dam type selection

(2). Understand the role of ancillary works in the dam

(3). Identify and estimate the various forces acting on the dam

(4). Perform both static and dynamic analysis as part of design process

2

Reference: Novak, P., Moffat, I.B. and Nalluri, Hydraulic structures, 4th ed

WHAT IS A DAM?

� A dam is a barrier built across a stream, river or estuary to holdand control the flow of water for uses such as drinking watersupplies, irrigation, flood control and hydropower generationetc.

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WHAT IS A DAM?

4http://www.fs.fed.us/eng/pubs/htmlpubs/htm12732805/longdesc/fig01ld.htm

WHAT IS A DAM?

5

AERIAL POV Bullards bar reservoir and new bullards bar dam, California

http://www.gettyimages.ae/detail/video/bullards-bar-reservoir-and-new-bullards-bar-dam-stock-video-footage/594215033

WHAT IS A DAM?

6

Tygart River Dam

BENEFITS OF DAMS� The benefits of dams are usually to the advantage of humans. They

may include:

� Irrigation

� Hydro-electric production

� Flood control

� Recreational opportunities

� Navigation

� Industrial and Domestic water supply

� Aeration of water

� For animals the benefits may include:

� Larger numbers of fish and birds in the reservoir

� Greater habitat diversity

7

DISADVANTAGES OF DAMS

Impacts on Environmental and Ecosystem of the area

• Changes in temperature and flow/sediment transport in the riverdownstream from the dam

• Loss of flowing water habitat and replacement with standingwater (reservoir) habitat

• Interruption of animal movements along the course of the river

• Possible alteration of the fish community in the region of theriver

• Interruption of genetic exchange among populations inhabitingthe river course

• Reduction in the delivery of river nutrients to downstreamsection of the river because of entrapment by the reservoir

• The loss of the floodplain habitat and connectivity between theriver and bordering habitats upland

8

PURPOSE DISTRIBUTION OF DAMS

Source: International Commission on Large Dams (ICOLD)

http://www.icold-cigb.net

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PURPOSE DISTRIBUTION OF DAMS

Source: International Commission on Large Dams (ICOLD)

http://www.icold-cigb.net/

10

CLASSIFICATION OF DAMS:

Dams are classified on several aspects, some of the important aspects are as follow:

1) Based on Hydraulic Design:

� Over flow dams (e.g. concrete dams)

� Non over flow dams (e.g. embankment dams)

2) Based on Structural Design:

� Gravity dams

� Arch dams

� Buttress dams

3) Based on Usage of Dam:

� Storage dams

� Diversion dams

� Detention dams

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CLASSIFICATION OF DAMS:

4) Based on Construction Material:

� Concrete / Masonary dams

� Earthfill dams

� Rockfill dams

� Earth and rockfill dams

� Concrete faced rockfill dams (CFRD)

5) Based on Capacity:

� Small dams

� Medium dams

� Large dams

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TYPES OF STORAGE DAMS

(1). Embankment Dams: Constructed of earth-fill and/or rock-fill.Upstream and downstream face slopes are similar and ofmoderate angle, giving a wide selection and high constructionvolume relative to height.

(2). Gravity Dams: Constructed of mass concrete. Face slopes aredissimilar, generally steep downstream and near vertical upstreamand dams have relatively slender profiles depending upon type

Note: Embankment dams are numerically dominant for technical andeconomical reasons, and account for over 85-90% of all dams built

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Concrete Dams

• Gravity DamThese dams resist the horizontalthrust of the water entirely by theirown weight. These are typicallyused to block streams throughnarrow gorges.

• Buttress DamIn these dams, the face is held upby a series of supports. It cantake many forms -- the face maybe flat or curved.

• Arch DamIt is a curved dam which isdependent upon arch action for itsstrength. Arch dams are thinnerand therefore require lessmaterial than any other type ofdam.

� Embankment Dams

� Earth-fill Dam

� These, also called earthen,rolled-earth or simply earthdams, are constructed as asimple embankment of wellcompacted earth.

� Rock-fill Dam

� These are embankments ofcompacted free-draininggranular earth with animpervious zone. The earthutilized often contains a largepercentage of large particleshence the term rock-fill isused.

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Embankment damGravity dam

Arch damButtress dam

15

TYPES OF DAMS

http://www.icold-cigb.net/

18

Following are the important factors considered for the selection of sitefor a dam:

SITE SELECTION OF A DAM

1) Catchment characteristics

2) Length of dam

3) Height of dam

4) Foundation conditions

5) Availability of suitable Spillway location

6) Availability of suitable construction materials

6) Storage capacity

7) Construction and maintenance cost

8) Access to the site

9) Options for diversion of river during construction

10) Compensation cost for property and land acquisition

11) Quality of water

12) Sediment transport

13) Environmental conditions

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The choice of dam is decided upon by examining foundation conditions,load strains, temperature and pressure changes, chemicalcharacteristics of ground water and possible seismic activity.

The followings important factors are considered for the selection of typeof dams:

SELECTION OF DAM TYPE

1) Topography

2) Geology and nature of foundation� Bearing capacity of the underlying soil

� Foundation settlements

� Permeability of the foundation soil

� Foundation excavation

3) Hydraulic Gradient

4) Availability of construction materials

5) Economics

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6) Spillway location

7) Safety considerations

8) Earthquake zones

9) Purpose of dam

10)Aesthetic considerations

11)Life of the Dam

SELECTION OF DAM TYPE

The optimum type of dam for a specific site is determined by estimates of cost and construction programme for all design solutions which are technically valid.

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STAGES FOR DAM SITE APPRAISAL

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24

ANCILLARY WORKS

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ANCILLARY WORKS

� Dams require certain ancillary structures and facilities to enablethem to discharge their operational function safely and effectively.

� In particular, adequate provision must be made for the safepassage of extreme floods and for controlled draw-off anddischarge of water in fulfillment of the purpose of the reservoir.

� Spillways, outlets and ancillary facilities are incorporated asnecessary for the purpose of the dam and appropriate to its type.

Ancillary works includes construction of spillways, stilling basins, culverts or tunnels for outlet works, valve towers etc. It also include crest details e.g., roadway, drainage works, wave walls etc.

26

SPILLWAYS

� Spillways: The purpose of spillway is to pass flood watersafely downstream when the reservoir is full.

� The Spillways can be� Uncontrolled (Normally)

�Controlled

� Note: Concrete dams normally incorporate an over-fall orcrest spillway, but embankment dams generally require aseparate side-channel or shaft spillway structure locatedadjacent to the dam.

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Types of Spillways

a. Overflow spillways

b. Chute spillways

c. Side-channel spillways

d. Shaft spillways

e. Siphon spillways

f. Service & Emergency spillways

SPILLWAYS

Acknowledgment: Some text and pictures are taken from the lecture notes of

Clayton J. Clark II (Department of Civil & Coastal Engineering, Gainesville,

Florida) http://www.ce.ufl.edu/~clark/28

OVERFLOW SPILLWAYS

Section of a dam that allows water to pass over its crest widely used on gravity, arch, & buttress dam

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CHUTE SPILLWAYS

Auxiliary Spillway of Tarbela Dam Service Spillway of Tarbela Dam

formed by spillways that flow over a crest into a steep-sloped open channel*chute width is often constant: -narrowed for economy

-widened to decrease discharge velocity

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SIDE CHANNEL SPILLWAYS

Spillway in which flow, after passing over the crest, is carried away ina channel running parallel to the crest

* used in narrow canyons in which there is sufficient crest lengthfor overflow or chute is available

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SHAFT SPILLWAY

Shaft spillway at Ladybower Reservoir

Water drops through a vertical shaft in a the foundation material to a horizontal conduit that conveys the water past the dam

*often used where there is not room enough for other spillways*possible clogging with debris a potential problem; screens and trashracks protect inlet

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SIPHON SPILLWAY

Siphon PrincipleTypical Siphon Spillway

Air vent used automatically maintain the water-surface elevationlarge capacity not needed, good for limited space

* At low flow: it acts like an overflow spillway* At high flow: the siphon action removes the water through the structure until reservoir drops to the elevation at the upper lip of entrance

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SERVICE AND EMERGENCY SPILLWAY

Submerged Orifice type Spillway at Mangla Dam

Service and Emergency Spillways-extra spillways provided on a project in rare case of extreme floods (emergency)-used to convey frequently occurring outflow rates (service)

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SPILLWAY, OUTLETS AND ANCILLARY WORKS

� Outlet Works:

� Controlled outlets are requiredto permit water to be drawn offas is operationally necessary.

� Provision must be made toaccommodate the requiredpenstocks and pipe works withtheir associated control gatesor valves.

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SPILLWAYS, OUTLETS AND ANCILLARY WORKS

� River Diversion:

� Necessary to permit construction to proceed in dry conditions

� An outlet tunnel may be adapted to this purpose during constructionand subsequently employed as a discharge facility for the completeddam.

� Alternate of such tunnels can be coffer dams.

� Cut-offs:

� Used to control seepage around and under the flank of dams.

� Embankment cut-offs are generally formed by

� Wide trenches backfilled with rolled clay,

� Grouting to greater depths

� Grout Screen cut-offs in rock foundations

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� Internal Drainage:

� Seepage is always present within the body of dam. Seepage flowsand their resultant internal pressures must be directed andcontrolled.

� In embankment dams, seepage is effected by suitably locatedpervious zones leading to horizontal blanket drains or outlets atbase level

� In concrete dams vertical drains are formed inside the upstreamface, and seepage is relieved into an internal gallery or outlet drain.

� In arch dams, seepage pressure in rock abutments are frequentlydrained by purpose built system of drainage ducts

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The tunnels inside the dam for control of seepage and monitoring structural stability

Seepage Control in Concrete Dams

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� Internal Galleries and Shafts

� Galleries and shafts are provided as means of allowing internalinspection, particularly in concrete dams.

� These can be used to accommodate structural monitoring andsurveillance purpose.

Internal gallery at concrete-gravity dam inspected by D'Appolonia. 39

FORCES ON DAMS

Primary Loads are identified as universally applicable and of prime importance to all dams, irrespective of type, e.g. water and related seepage loads, and self-weight loads.

Secondary loads are generally discretionary and of lesser magnitude (e.g. sediment load) or, alternatively, are of major importance only to certain types of dams (e.g. thermal effects within concrete dams).

Exceptional Load are so designated on the basis of limited general applicability or having a low probability of occurrence. (e.g. tectonic effects, or the inertial loads associated with seismic activity)

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FORCES ON DAMS

The primary loads and the more important secondary and exceptional sources of loading are identified schematically on Fig. a gravity dam section being used for this purpose as a matter of illustrative convenience.

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FORCES ON DAMS

Primary Loads:

(a): Water Load: This is a hydrostatic distribution of pressure with

horizontal resultant force P1. (Note that a vertical component of load will also exist in the case of an upstream face batter, and that equivalent tailwater loads may operate on the downstream face.)

(b): Self Weight load: This is determined with respect to an

appropriate unit weight for the material. For simple elastic analysis the resultant, P2, is considered to operate through the centroid of the section.

(c): Seepage Loads: Equilibrium seepage patterns will develop

within and under a dam, e.g. in pores and discontinuities, with resultant vertical loads identified as internal and external uplift, P3 and P4, respectively.

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FORCES ON DAMSSecondary Loads:

(a): Sediment load: Accumulated silt etc. generates a horizontal thrust,

considered as an equivalent additional hydrostatic load with horizontal

resultant P5.

(b): Hydrodynamic wave load: This is a transient and random local load,

P6, generated by wave action against the dam (not normally significant).

(c): Ice Load: Ice thrust, P7, from thermal effects and wind drag, may

develop in more extreme climatic conditions (not normally significant).

(d): Thermal Load: (concrete dams), This is an internal load generated by

temperature differentials associated with changes in ambient conditions and

with cement hydration and cooling (not shown).

(e): Interactive effect: Internal, arising from relative stiffness and differential

deformations of dam and attributable to local variations in foundation stiffness

and other factors, e.g. tectonic movement (not shown).

(f): Abutment hydrostatic load: Internal seepage load in abutment rockmass ( This is of particular concern to arch and cupola dams)

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FORCES ON DAMS

Exceptional Load:

(a): Seismic Load: Oscillatory horizontal and vertical inertia loads

are generated with respect to the dam and the retained water by seismic disturbance. For the dam they are shown symbolically to act through the section centroid. For the water inertia forces the simplified equivalent static thrust, P8, is shown

(b): Tectonic Loads: Saturation, or disturbance following deep

excavation in rock, may generate loading as a result of slow tectonic movements.

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LOAD COMBINATION

A dam is designed for the most adverse combinations of loads as theyhave reasonable probability of simultaneous occurrence.

For construction conditions: Dam is completed, reservoir is empty,no tail water

i. With earthquake forces

ii. Without earthquake forces

For normal operating conditions; reservoir full, normal tail waterconditions, normal uplifts and silt load



For flood discharge conditions: reservoir at max flood level, allspillway gates open, tail water at flood levels, normal uplifts and siltload

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GRAVITY DAM ANALYSIS

• CRITERIA AND PRINCIPLES

• The dam profile must demonstrate an acceptable margin of safety with regard to

• 1. Rotation and overturning,

• 2. Translation and sliding and

• 3. Overstress and material failure.

• Criteria 1 and 2 control overall structural stability. Both must be satisfied with respect to the profile above all horizontal planes within the dam and the foundation. The overstress criterion, 3, must be satisfied for the dam concrete and for the rock foundation.

• The sliding stability criterion, 2, is generally the most critical of the three, notably when applied to the natural rock foundation.

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SAFETY CRITERIA

1. Safety against Overturning

2. Safety against Sliding

3. Safety against Crushing

4. Safety against Tension

Dams are not designed to take any tension load.

Safety factors must be more than permissible under all load combinations

47

DISCUSSION ON THE

CALCULATION OF FORCES ACTING

ON CONCRETE (GRAVITY) DAM

CONCRETE DAM ENGINEERING

48

For further reading:Novak, P., Moffat, I.B. and Nalluri, Hydraulic structures, 4th ed

GRAVITY DAM: LOADING CONCEPTS

Fig. Gravity dam loading diagram. DFL=Design flood level;

NML=Normal maximum level, i.e. maximum retention level of spill weir;

TWL=Tailwater level

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GRAVITY DAM: LOADING CONCEPTS(A) PRIMARY LOADS

• WATER LOAD

• The external hydrostatic pressure, Pw, at depth z1 is expressed as

• where γw is the unit weight of water, 9.81kN/m3

• The resultant horizontal force, Pwh, is determined as

• acting at height z1/3 above plane X–X.

A resultant vertical force Pwv must

also be accounted for if the

upstream face has a slope, as with

the profile above

and acts through the centroid of A1

Similar to u/s, the corresponding resultant forces Pwh’ and Pwv’ at d/s operative above

the toe, can also be calculated. 50


• SELF LOAD

• Self-weight of structure is accounted for in terms of its resultant, Pm, which is considered to act through the centroid of the cross-sectional area Ap of the dam profile

• γc is the unit weight of concrete, assumed as 23.5kN/m3 in the absence of specific data from laboratory trials or from core samples.

Where crest gates and other ancillary

structures or equipment of significant

weight are present they must also be

accounted for in determining Pm and

the position of its line of action.

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• SEEPAGE AND UPLIFT LOAD: Uplift load, Pu, is represented by the resultant effective vertical components of interstitial water pressure uw.

• Uplift pressure at u/s=γwz1 and uplift pressure at d/s γwz2

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• SEEPAGE AND UPLIFT LOAD

• If no pressure relief drains are provided or if they cease to function owing to leaching and blockage, then

• Where T is base area per unit base thickness.

• Pu acts through the centroid of the pressure distribution diagram at distance y1 from the heel, and

T

In modern dams internal uplift is

controlled by the provision of vertical

relief drains close behind the

upstream face. The mean effective

head at the line of drains, zd, can be

expressed as

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GRAVITY DAM: LOADING CONCEPTS(B) SECONDAY LOADS

• SEDIMENT LOAD

• The magnitude of sediment load, Ps, is given by

• Where, z3 is sediment depth, γs’ is the submerged unit weight of sediment and the Ka

is the active lateral pressure coefficient and ϕs is the angle of shearing resistance of the sediment

• Ps is active at z3/3 above plane X–X.

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• HYDRODYNAMIC WAVE LOAD

• It is considered only in exceptional cases. Pwave is necessary a conservative estimate of additional hydrostatic load at the reservoir surface is provided by

• Hs is the significant wave height, i.e. the mean height of the highest third of waves in a sample, and is reflected at double amplitude on striking a vertical face

55


• ICE LOAD

• Ice load can be introduced in circumstances where ice sheets form to appreciable thicknesses and persist for lengthy periods.

• According to USBR, 1976, acceptable initial provision for ice load is given below:

• Pice=145kN/m2 if ice thicknesses > 0.6 m

• Pice=0 if ice thickness < 0.4m

56


• THERMAL AND DAM–FOUNDATION INTERACTION EFFECTS

• Beyond the scope of our course and comprehensively discussed in USBR (1976).

57

GRAVITY DAM: LOADING CONCEPTS(C) EXCEPTIONAL LOADS

• SEISMICITY AND SEISMIC LOAD

• Concrete dams are quasi-elastic structures and are intended to remain so at their design level of seismic acceleration. They should also be designed to withstand an appropriate maximum earthquake, e.g. CME (controlling maximum earthquake) or SEE (safety evaluation earthquake) (Charles et al., 1991) without rupture.

• Seismic loads can be approximated using the simplistic approach of pseudostatic or seismic coefficient analysis. Inertia forces are calculated in terms of the acceleration maxima selected for design and considered as equivalent to additional static loads. This approach, sometimes referred to as the equivalent static load method, is generally conservative.

58


• SEISMICITY AND SEISMIC LOAD: PSEUDOSTATIC ANALYSIS

• INERTIA FORCES: MASS OF DAM

• Pseudostatic inertia and hydrodynamic loads are determined from seismic coefficients αh and αv as detailed below.

• As with self-weight load, Pm, inertia forces are considered to operate through the centroid of the dam section. The reversible direction of the forces will be noted; positive is used here to denote inertia forces operative in an upstream and/or a downward sense

59



• HYDRODYNAMIC INERTIA FORCES: WATER REACTION.

• An initial estimate of these forces can be obtained using a parabolic approximation to the theoretical pressure distribution as analyzed in Westergaard (1933).

• Relative to any elevation at depth z1 below the water surface, hydrodynamic pressure pewh is determined by

• In this expression zmax is the maximum depth of water at the section of dam considered. Ce is a dimensionless pressure factor, and is a function of z1/zmax and ϕu, the angle of inclination of the upstream face to the vertical.

• The resultant hydrodynamic load is given by:

• and acts at elevation 0.40z1 above X–X.60

Check the formula !!




• Indicative values of Ce are given in Table.

• As an initial coarse approximation, hydrodynamic load Pewh is sometimes equated to a 50% increase in the inertia load, Pemh.

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• Zanger Formula





• The resultant vertical hydrodynamic load, Pewv, effective above an upstream face batter or flare may be accounted for by application of the appropriate seismic coefficient to vertical water load, Pwv. It is considered to act through the centroid of area A1 thus:

• Uplift load is normally assumed to be unaltered by seismic shock in view of the latter’s transient and oscillatory nature.

63

LOAD COMBINATIONS

A dam is designed for the most adverse combinations of loads as theyhave reasonable probability of simultaneous occurrence.

For construction conditions: Dam is completed, reservoir is empty,no tail water



For normal operating conditions: reservoir full, normal tail waterconditions, normal uplifts and silt load



For flood discharge conditions: reservoir at max flood level, allspillway gates open, tail water at flood levels, normal uplifts and siltload

64

LOAD COMBINATIONS

The nominated load

combinations as defined in

the table are not universally

applicable. An obligation

remains with the designer to

exercise discretion in defining

load

combinations which properly

reflect the circumstances of

the dam under

consideration, e.g.

anticipated flood

characteristics, temperature

regimes,

operating rules, etc.

65







• Criteria 1 and 2 control overall structural stability. Both must be satisfied with respect to the profile above all horizontal planes within the dam and the foundation. The overstress criterion, 3, must be satisfied for the dam concrete and for the rock foundation.

• The sliding stability criterion, 2, is generally the most critical of the three, notably when applied to the natural rock foundation.

66




Stabilizing MomentFOS

Overturning Moment

∑=∑

67

These moments are calculated at toe of the dam



• 2. Translation and sliding

• Slide safety is conventionally expressed in terms of a factor of safety, FOS, or stability factor against sliding, FS, estimated using one or other of three definitions:

• i. Sliding factor, FSS;

• ii. Shear friction factor, FSF;

• iii. Limit equilibrium factor, FLE.

• The resistance to sliding or shearing, which can be mobilized across a plane, is expressed through the twin parameters C and tanϕ.

• Cohesion, C, represents the unit shearing strength of concrete or rock under conditions of zero normal stress. The coefficient tanϕrepresents frictional resistance to shearing, where is the angle of shearing resistance or of sliding friction,

68




69




70



• 2. translation and sliding

71





• For plane surface

• For inclined surface at a small angle ,

Applied to well-constructed mass concrete, FSS on a horizontal plane

should not be permitted to exceed 0.75 for the specified normal load

combination. FSS may be permitted to rise to 0.9 under the extreme

load combination.

72




• ii. Shear Friction Factor, FSF: It is defined as the ratio of the total resistance to shear and sliding which can be mobilized on a plane to the total horizontal load.

For inclined plane

For horizontal plane

Ah is the thickness, T,for a two-dimensional section).i,e.,

Ah=T

73




• ii. Shear Friction Factor,

• In some circumstances it may be appropriate to include downstream passive wedge resistance, Pp, as a further component of the total resistance to sliding which can be mobilized.

WW is the weight of the passive wedge

74




• ii. Shear Friction Factor,

75




• iii. Limit Equilibrium Factor, FLE: It is the ratio of shear strength to mean applied shear stress across a plane:

• Note that for the case of a horizontal sliding plane (α=0), equation simplifies to the expression given for FSF, i.e. FLE=FSF(α=0).

• Recommended FLE=2.0 in normal operation, i.e. with static load maxima applied, and FLE=1.3 under transient load conditions embracing seismic activity.

76




• It must be stressed that values for FSS, FSF and FLE cannot be directly correlated.

• The stability factor and sliding criteria most appropriate to a specific dam are determined by the designer’s understanding of the conditions

77




• The primary stresses determined in a comprehensive analysis by the gravity method are as follows:

• 1. vertical normal stresses, σz, on horizontal planes;

• 2. horizontal and vertical shear stresses, σzy and σyz;

• 3. horizontal normal stress, τy, on vertical planes;

• 4. major and minor principal stresses, σ1 and σ3 (direction and magnitude).

78




79




• (a) Vertical normal stresses

where e is the eccentricity of the

resultant load, R, which must

intersect the plane downstream

of its centroid for the reservoir

full condition.

80




• (b) Horizontal shear stresses

• If the angles between the face slopes and the vertical are respectively Φu upstream and Φ d downstream, and if an external hydrostatic pressure, pw, is assumed to operate at the upstream face, then

81




• (c) Horizontal normal stresses

82




• (d) Principal stresses

• The boundary values for σ1 and σ3 are then determined as follows

83




84

SAFETY CRITERIA: SUMMARY

Safety against Overturning:

Safety against Sliding:

Safety against Crushing:

Safety against Tension:

Dams are not designed to take any tension load.

Stabilizing MomentFOS

Overturning Moment

∑=∑

85

PROBLEM:

A concrete gravity dam has the following dimensions:

�Max water level = 305 m

�Bed level of river = 225 m

�Crest level = 309 m

�D/S face slope starts at 300 m

�D/S Slope= 2:3

�C/L of drainage galleries at 8m d/s of u/s face

�Uplift pressures:

at Heal = 100 %

at Toe = 0 %

at drainage gallery = 50 %

86

PROBLEM:�Density of concrete = 2400 kg/m3

�No tail water

�Foundation condition: inferior condition with limestone

�Consider self weight, hydrostatic pressure and uplift pressure

Check the stability of dam for

•1. Rotation and overturning,

•2. Translation and sliding and

•3. Overstress and material failure.

87

SOLUTION

8m

α

309 m

300 m

W.L 305 m

2

3

B.L. 225 m

Wc

88

8m

α

309 m

300 m

W.L 305 m

2

3

B.L. 225 m

Determine width of crest, Wc=?

m

Wc

Wc

1216.9

84225309

DamofHeight

≈=

=−=

=

80m

84m

75m

12m

heal

toe

89

8m

α

309 m

300 m

W.L 305 m

2

3

B.L. 225 m

WATER LOAD

80m

84m

1/3*80=26.67m

75m

50m12m

Pwh

12m

56mheal

toe

( )

tons

hP

mtonhp

wwh

ww

3200

22530512

1

2/

/80)80(1

2

2

2

=

−××=

=

===

γ

γ

33 /1/1000 mmtonmkgw ==γ

where

Acting at h/3 i.e., 26.67m from BL

in horizontal direction

33.33m

Since there is no tail water therefore Pwh’=0

90

8m

α

309 m

300 m

W.L 305 m

2

3

B.L. 225 m

SELF LOAD

80m

84m

75m

50m12m

W1 W2tons

W

2.2419

1000/240084121

=

××=

12m

56mheal

toe

Acting 56m from toe

tons

W

4500

1000/240050752

12

=

×××=

Acting 33.33m from toe

50m

33.33m

Divide the dam into regular shaped segments and calculate total load and point of application

tonsWWPm 2.691945002.241921 =+=+=91

8m

α

309 m

300 m

W.L 305 m

2

3

B.L. 225 m

The uplift pressure without drainagegalleries is represented by dash line.However, the drainage galleriescontrol the pressure distribution andin present problem, the upliftpressure at drainage gallery is givenas 50% of total uplift pressure h=80m

84m

1/3*80=26.67m

75m

50m12m

W1 W2

Pwh

12m

heal toe

Without drainage galleries

With drainage galleries

100%=γwh 50%=0.5γwh

SEEPAGE AND UPLIFT LOAD

The uplift pressure at the heal istaken equal to heal of water. i.e., γwhΓwx80.While at the drainage gallery it is50% of γwx80. i.e., γwx40And at the toe it becomes zero asthere is no tail water.

where

h=80m

γw=1000kg/m3=1mton/m3

92

8m

α

309 m

300 m

W.L 305 m

2

3

B.L. 225 m

80m

84m

1/3*80=26.67m

75m

50m12m

W1 W2

Pwh

12m

heal toe

U2

U1 U3

ton

hU w

32088015.0

85.01

=×××=

×= γ

100%=γwh

50%=0.5γwh

( )

( ) ton

hU w

16088015.05.0

85.05.02

=×××=

×= γ

( ) ( )

( ) ton

hU w

1080548015.05.0

4505.05.03

=×××=

+×= γ

Acting 58m from toe

Acting 59.33m from toe

Acting 36m from toe

58 m

59.33 m

36 m

ton

UUUPu

15601080160320

321

=++=

++=

Net uplift forces

SEEPAGE AND UPLIFT LOAD

93

• SECONDARY LOADS

• Sediment load-nil

• Hydrodynamic load-nil

• Ice load-nil

• Thermal loads-nil

• EXCEPTIONAL LOAD

• Seismic load-nil

94






• ii. Shear friction factor, FSF;

• iii. Limit equilibrium factor, FLE.


95

1. Stability against Rotation and Overturning

momentgOverturnin

momentgStabilizinFOS =

Taking moment at toe of dam

8m

α

309 m

300 m

W.L 305 m

2

3

B.L. 225 m

80m

84m

1/3*80=26.67m

75m

50m12m

W1 W2

Pwh

12m

heal toe

U2

U1 U3

58 m

59.33 m

36 m

5.187.1

67.2636333.59233.591

33.332561

>=

×+×+×+×

×+×=

FOS

PUUU

WWFOS

wh

It ranges from 1.5~2.5

96

2. Stability against sliding of dam

59.0

2.5359/3200

=

=

=∑∑

FOS

FOS

V

HFSS

It should not be permitted to exceed 0.75 for normal load combinations

i. Sliding factor, FSS;

8m

α

309 m

300 m

W.L 305 m

2

3

B.L. 225 m

80m

84m

1/3*80=26.67m

75m

50m12m

W1 W2

Pwh

12m

heal toe

U2

U1 U3

58 m

59.33 m

36 m

97


76.1

3200

2.53598.062)81.9/10003.0(

tan

=

×+×=

+==

∑∑

∑

SF

SF

h

SF

F

F

H

VcA

H

SF

φ

It ranges from 1.0 (extreme) ~ 3.0 (normal)

ii. Shear Friction Factor, FSF:

Foundation condition: Inferior condition with limestonetanΦ=0.7 and c=0.3MN/m2

(see slide 69)

Ah=T=B=62m

8m

α

309 m

300 m

W.L 305 m

2

3

B.L. 225 m

80m

84m

1/3*80=26.67m

75m

50m12m

W1 W2

Pwh

12m

heal toe

U2

U1 U3

58 m

59.33 m

36 m

98


176.1 >=LEF

FLE=1.3 (seismic) ~ 2.0 (normal)

iii. Limit Equilibrium Factor, FLE:

For plane surface

FLE=FSF

99


• The primary stresses determined in a comprehensive analysis by the gravity method are as follows:

a) vertical normal stresses, σz, on horizontal planes;

b) horizontal and vertical shear stresses, σzy and σyz;

c) horizontal normal stress, τy, on vertical planes;

d) major and minor principal stresses, σ1 and σ3 (direction and magnitude).

100

8m

α

309 m

300 m

W.L 305 m

2

3

B.L. 225 m

80m

84m

1/3*80=26.67m

75m

50m12m

W1 W2

Pwh

12m

heal toe

Eccentricity and position of resultant

U2

U1 U3100%=γwh

50%=0.5γwh

58 m

59.33 m

36 m

∑∑

=−=V

Mxwherex

Be ,,

2

ton.

-.-

-UWW

V

25359

1560224194500

21

forces verticalTotal

=

=

+=

=∑

m ton

P

UU-U

WW

M

−=

×−

×−×−×

×+×=

=∑

4.133183

67.26

36333.592581

33.332561

at toemoment Total

position of resultant

mx 85.242.5359

4.133183==

B is the based width of dam=62m

101

8m

α

309 m

300 m

W.L 305 m

2

3

B.L. 225 m

80m

84m

1/3*80=26.67m

75m

50m12m

W1 W2

Pwh

12m

heal toe

Eccentricity and position of resultant

U2

U1 U3100%=γwh

50%=0.5γwh

58 m

59.33 m

36 m

∑∑

=−=V

Mxwherex

Be ,,

2

mx 85.242.5359

4.133183==

3

B

mB

33.103

=3

B

m

xB

e

15.6

85.242

62

2

=

−=−=

6

B

6

B

6/Be <

e

tension will develop !

Note: The resultant must pass through the middle third

6/Be >If

Dam is unsafe again tension. Size of dam can be increased to enhance stability

102

(a). Vertical normal stresses

2

min

2

max

/99.34

62

15.6*61

62

2.5359

61

/89.137

62

15.6*61

62

2.5359

61

mton

B

e

B

VP

mton

B

e

B

VP

zu

zd

=

−=

−==

=

+=

+==

∑

∑

σ

σ

Normal shear stress at toe

Normal shear stress at heal

Allowable stress=25 kg/cm2

=250 ton/m2

Therefore, dam is safe against tension and compression103

(b). Horizontal shear stresses

( )

( ) 00tan

tan

=−=

−=

zuw

uzuwu

p

p

σ

φστ

Shear stress at upstream (heal)

Shear stress at downstream (toe)

( )

( ) 2/93.91)3/2(89.137

tan

mton

dzdd

==

= φστ

104

(c). Horizontal normal stresses

( )

( )2

2

2

/28.61

)3/2(89.137

tan

mton

dzdyd

=

×=

= φσσ

Shear stress at downstream face (toe)

( )

( )2

2

2

/80

0tan80

tan

mton

p

pp

wzu

uwzuwyu

=

−+=

−+=

σ

φσσ

Shear stress at upstream face (heal)

105

(d). Principal stresses

For upstream face (heal)

For downstream face (toe) with no tail water (pw’=0)

( )( )

2

3

3

2

22

1

22

1

/80

/99.34

0tan0tan199.34

tantan1

mton

p

mton

p

p

u

wu

wu

uwuzuu

=

=

=

−+=

−+=

σ

σ

σ

φφσσ

( )( )

0

'

/16.199

)3/2(189.137

tan'tan1

3

3

2

21

221

=

=

=

+=

−+=

d

wd

d

dwdzdd

p

mton

p

σ

σ

σ

φφσσ

106

PROBLEM:A concrete gravity dam has the following dimensions:

�Max water level = 305 m

�Bed level of river = 225 m

�Crest level = 309 m

�U/S slope starts at 305 m

�U/S slope = (H:V)= 0.5:1

�D/S face slope starts at 300 m

�D/S Slope= (H:V)= 2:3

�C/L of drainage galleries at 8m d/s of u/s face

�Uplift pressures:

at Heal = 100 %

at Toe = 0 %

at drainage gallery = 50 %

107

PROBLEM 2:

�Density of concrete = 2400 kg/m3

�No tail water

�Consider self weight, hydrostatic pressure and uplift pressure

Check the stability of dam for

•1. Rotation and overturning,

•2. Translation and sliding and

•3. Overstress and material failure.

108

PROBLEM 2:

8m

α

309 m

300 m

W.L 305 m

2

3

B.L. 225 m

Wc

1

0.5

109

PROBLEM 3

Figure (on next slide) shows a section of a gravity dam built of concrete, examine the static and dynamic stability of this section at the base for the following cases

1. Reservoir is full and no seismic force is acting

2. Reservoir is full and seismic forces are acting

The earthquake forces may be taken as equivalent to 0.1g for horizontal and 0.05g for vertical forces. The uplift may be taken as equal to the hydrodynamic pressure at either end and is considered to act over 60% of the area of the section at base.

A tail water of 6m is assumed to be present when the reservoir is full and there is no tail water when the reservoir is empty.

Also calculate the various kinds of forces at the heal and toe of the dam.

Assume the unit weight of concrete=24kN/m3 and unit weight of water=10kN/m3

PROBLEM 3

Date of submission: Nov 30, 2016

THANK YOU