CVECVE 471471 WATERWATER RESOURCESRESOURCES ENGINEERINGENGINEERING
DAMSDAMS
Assist. Prof. Dr. Bertuğ Akıntuğ
Civil Engineering Program Middle East Technical University Northern Cyprus Campus
CVE 471 Water Resources Engineering 1/101 3. DAMS
Overview
Classification of Dams
Parts of Dams
Planning of Dams
Construction of Dams
Concrete Gravity Dams
Arch Dams
Cross-sectional Layout Design of Dams
Local Scour at the Downstream of Dams
Dam Safety and Rehabilitation
CVE 471 Water Resources Engineering 2/101 3. DAMS
Overview
Classification of Dams
Parts of Dams
Planning of Dams
Construction of Dams
Concrete Gravity Dams
Arch Dams
Buttress Dams
Embankment (Fill Dams)
Cross-sectional Layout Design of Dams
Local Scour at the Downstream of Dams
Dam Safety and Rehabilitation
CVE 471 Water Resources Engineering 3/101 3. DAMS
Classification of Dams
A dam is an impervious barrier built across a watercourse to store water for several purposes:
water supply,
creating head (energy generation),
forming a lake,
sediment control,
flood control,
recharging of groundwater, etc.
There are disadvantages of dams as well:
imbalance of ecosystem,
decrease amount of downstream water,
reduction in the fertility of farmlands, etc.
Therefore, detailed survey should be carried out to ensure that the relative weights of advantages over disadvantages are higher.
CVE 471 Water Resources Engineering 4/101 3. DAMS
Classification of Dams
Dams can be classified into a number of different categories depending upon the purpose of classifications.
A classification based on the type and materials of construction:
Gravity Dams
Concrete gravity dams
Prestressed concrete gravity dams
Roller compacted concrete (RCC) gravity dams
Arch Dams
Constant-angle arch dams
Constant-center arch dams
Variable-angel, variable-cemter arch dams
Buttress Dams
Flat-slab buttress dams
Multiple-arch buttress dams
Embankment (Fill) Dams
CVE 471 Water Resources Engineering 5/101 3. DAMS
Classification of Dams
Gravity Dams
Concrete gravity dams
Pre-stressed concrete gravity dams
Roller compacted concrete (RCC) gravity dams
Karun Dam, Iran http://en.wikipedia.org/wiki/Dam
Shasta Dam, California, USA CVE 471 Water Resources Engineering 6/101 3. DAMS
Classification of Dams
Arch Dams
Constant-angle arch dams
Constant-center arch dams
Variable-angel arch dams
Variable-center arch dams
Monticello Dam, California, USA Gordon Dam, Tasmania http://en.wikipedia.org/wiki/Dam CVE 471 Water Resources Engineering 7/101 3. DAMS
Classification of Dams
Buttress Dams Used mainly in wide valleys, it consists of an impermeable wall, which is shored up by a series of buttresses to transmit the thrust of the water to the foundation.
Flat-slab buttress dams
Multiple-arch buttress dams
CVE 471 Water Resources Engineering 8/101 3. DAMS
Classification of Dams
Buttress Dams
Flat-slab buttress dams
Lake Tahoe Dam, California, USA
CVE 471 Water Resources Engineering 9/101 3. DAMS
Classification of Dams
Buttress Dams
Multiple-arch buttress dams
Bartlett Dam , Phoenix, Arizona, USA
CVE 471 Water Resources Engineering 10/101 3. DAMS
Classification of Dams
Embankment (Fill) Dams
Earth-fill dams
Simple embankment
Zoned embankment
Diaphragm type embankment
Upstream of Ataturk Dam, Turkey
Embankment (Fill) Dams
Rock-fill dams
Downstream of Ataturk Dam, Turkey Impermeable-face
Impermeable-earth core CVE 471 Water Resources Engineering 11/101 3. DAMS
Classification of Dams
A classifications based on purpose, such as
storage
diversion
flood control
hydropower generation
A classification based on hydraulic design such as
overflow dams,
non-overflow dams Gilboa Dam, New York State, USA http://en.wikipedia.org/wiki/Dam
CVE 471 Water Resources Engineering 12/101 3. DAMS
Classification of Dams
A timber crib dam in Michigan, USA 1978 Liberty Dam, USA http://en.wikipedia.org/wiki/Dam
CVE 471 Water Resources Engineering 13/101 3. DAMS
Classification of Dams
A classification based on dam height:
According to the International Commission on Large Dams (ICOLD):
Large Dam Æ if height > 15 m
Large Dam Æ if 10 m < height < 15 m reservoir storage > 106 m3 crest length > 500 m
High Dam Æ height > 50 m
Small Dam Æ height < 10 m
Distribution of dam heights in Turkey as of 2002.
CVE 471 Water Resources Engineering 14/101 3. DAMS
Classification of Dams
Percent distribution of dams in Turkey according to purpose
CVE 471 Water Resources Engineering 15/101 3. DAMS
Overview
Classification of Dams
Parts of Dams
Planning of Dams
Construction of Dams
Concrete Gravity Dams
Arch Dams
Buttress Dams
Embankment (Fill Dams)
Cross-sectional Layout Design of Dams
Local Scour at the Downstream of Dams
Dam Safety and Rehabilitation
CVE 471 Water Resources Engineering 16/101 3. DAMS
Parts of Dams
A dam is composed of the following structural components
Body forms the main part of a dam as an impervious barrier.
Reservoir is the artificial lake behind a dam body.
Spillway is that part of a dam to evacuate the flood wave from the reservoir.
Water intake is a facility to withdraw water from a reservoir.
Outlet facilities are those appurtenances to withdraw water from the reservoir to meet the demands or to discharge the excess water in the reservoir to the downstream during high flows.
sluiceways,
penstocks,
diversion tunnels,
bottom outlets, and
water intake structures
Others: Hydropower station, site installations, roads, ship locks, fish passages, etc.
CVE 471 Water Resources Engineering 17/101 3. DAMS
Overview
Classification of Dams
Parts of Dams
Planning of Dams
Construction of Dams
Concrete Gravity Dams
Arch Dams
Buttress Dams
Embankment (Fill Dams)
Cross-sectional Layout Design of Dams
Local Scour at the Downstream of Dams
Dam Safety and Rehabilitation
CVE 471 Water Resources Engineering 18/101 3. DAMS
Planning of Dams
There are commonly three steps in the planning and design:
reconnaissance survey,
feasibility study, and
planning study.
In reconnaissance surveys, the alternatives, which seem infeasible without performing intensive study, are eliminated.
Feasibility Study:
Estimation of water demand
Determination of water potential
Optimal plans
Determination of dam site
Topography
Geologic information
Foundation conditions
Flood hazard
CVE 471 Water Resources Engineering 19/101 3. DAMS
Planning of Dams
Feasibility Study:
Determination of dam site (cont’d)
Spillway location and possibility
Climate
Diversion facilities
Sediment problem
Water quality
Transportation facilities
Right of way cost
Determination of type of dams
Project design
Hydrologic design
Hydraulic design
Structural design
CVE 471 Water Resources Engineering 20/101 3. DAMS
Planning of Dams
Planning Study:
Topographic surveys
Foundation studies
Details on materials and constructional facilities
Hydrologic study
Reservoir operation study
CVE 471 Water Resources Engineering 21/101 3. DAMS
Overview
Classification of Dams
Parts of Dams
Planning of Dams
Construction of Dams
Concrete Gravity Dams
Arch Dams
Buttress Dams
Embankment (Fill Dams)
Cross-sectional Layout Design of Dams
Local Scour at the Downstream of Dams
Dam Safety and Rehabilitation
CVE 471 Water Resources Engineering 22/101 3. DAMS
Construction of Dams
Details of dam construction are beyond the scope of this course.
The principal steps to be followed during the construction of any type of dam briefly:
Evaluation of time schedule and required equipment.
Diversion of river flow
Foundation treatment
Evaluation of Time Schedule and Required Equipment.
Items to be considered:
the characteristics of dam site
the approximate quantities of work
the preservation of construction equipment and materials
diversion facilities and urgency of work
CVE 471 Water Resources Engineering 23/101 3. DAMS
Construction of Dams
Diversion of River Flow Diversion of the river flow is may be accomplished in one of the following ways 1. Water is diverted through a side tunnel or channel.
(Applicable for low flow depths ~1.5 m)
Diversion by side tunnel or channel
CVE 471 Water Resources Engineering 24/101 3. DAMS
Construction of Dams
Diversion of River Flow (cont’d)
Typical cross-section of earth cofferdams
f: free board f=0.2(1+h)
h: flow depth (meters)
G=z/5 + 3 (meters)
Cofferdams should be constructed during the low flow season.
For fill type dams, embankment cofferdam may be kept in place as part of the embankment (e.g. Keban Dam and Ataturk Dam).
For concrete dams, embankment cofferdam should be demolished after the dam has been constructed.
Earth cofferdam on impervious foundation Earth cofferdam on pervious foundation CVE 471 Water Resources Engineering 25/101 3. DAMS
Construction of Dams
Diversion of River Flow (cont’d)
Hoover Dam, USA CVE 471 Water Resources Engineering 26/101 3. DAMS
Construction of Dams Diversion of River Flow (cont’d)
Hoover Dam Overflow Tunnels (spillways), USA
CVE 471 Water Resources Engineering 27/101 3. DAMS
Construction of Dams
Diversion of River Flow (cont’d)
Hoover Dam Overflow Tunnels (spillways), USA
CVE 471 Water Resources Engineering 28/101 3. DAMS Diversion of River Flow (cont’d)
Construction of Dams Hoover Dam Overflow Tunnels (spillways), USA
CVE 471 Water Resources Engineering 29/101 3. DAMS
Construction of Dams
Diversion of River Flow (cont’d) 2. Water is discharged through the construction, which takes place in two stages. This type of diversion is normally practiced in wider valleys.
Two-stage diversion
CVE 471 Water Resources Engineering 30/101 3. DAMS
Construction of Dams
Diversion of River Flow (cont’d)
Two-stage diversion
CVE 471 Water Resources Engineering 31/101 3. DAMS
Construction of Dams
Diversion of River Flow (cont’d)
A cofferdam on the Ohio River, Illinois, USA, built for the purpose of constructing the lock and dam. CVE 471 Water Resources Engineering 32/101 3. DAMS
Construction of Dams
Diversion of River Flow (cont’d)
Selection of a proper diversion scheme is based on the joint consideration of
hydrologic characteristics of river flow,
type of dam and its height,
availability of materials,
characteristics of spilling arrangements.
The optimum design is based on cost minimization.
The cost analysis is carried out for various sizes of diversion tunnels or channels to determine the corresponding total costs.
The optimum tunnel diameter or bottom width of a lined trapezoidal channel is then determined according to the minimum total cost of the facility.
CVE 471 Water Resources Engineering 33/101 3. DAMS
Construction of Dams
Foundation Treatment
Foundation treatment for dams is essential
to achieve less deformation under high loads,
to decrease permeability and seepage,
to increase shearing strength, and
to satisfy slope stability for the side hills.
Highly porous foundation material causes excessive seepage, uplift and considerable settlement.
Such problems can be improved by a grouting operation.
In this operation, the grout mix is injected under pressure to decrease the porosity, and hence to solidify the formations underlying the dam and reservoir.
CVE 471 Water Resources Engineering 34/101 3. DAMS
Overview
Classification of Dams
Parts of Dams
Planning of Dams
Construction of Dams
Concrete Gravity Dams
Arch Dams
Buttress Dams
Embankment (Fill Dams)
Cross-sectional Layout Design of Dams
Local Scour at the Downstream of Dams
Dam Safety and Rehabilitation
CVE 471 Water Resources Engineering 35/101 3. DAMS
Gravity Dams
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.
CVE 471 Water Resources Engineering 36/101 3. DAMS
Gravity Dams
Concrete Gravity Dams
Concrete gravity dams area built of mainly plain concrete to take compressive stresses.
Shasta Dam, California, USA
CVE 471 Water Resources Engineering 37/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d)
Concrete gravity dams have lower maintenance and operation costs compared to the other types of dams.
In the design of these structures, the following criteria should be satisfied:
Dimensions of the dam are chosen such that only compressive stresses develop under all loading conditions.
The dam must be safe against overturning, shear and sliding.
CVE 471 Water Resources Engineering 38/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d)
In the construction of concrete gravity dams special care is required for the problems due to shrinkage and expansion.
Formation of the body of the concrete gravity dam
CVE 471 Water Resources Engineering 39/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d) Forces Acting on Gravity Dams The weight:
Wc= dead load
Hydrostatic forces:
Uplift Force:
φ: uplift reduction coefficient
Moment arm of Fu=B(2h1+3h2) / 3(h1+h2)
Actual uplift pressures are determined by pressure gauges installed at the bottom of the dam. Free body diagram. Forces acting on a concrete gravity dam
CVE 471 Water Resources Engineering 40/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d) Forces Acting on Gravity Dams Sediment Force:
γs: submerged specific weight of soil Ka: active earth pressure coefficient according to the Rankine theory.
Ka = (1-sinθ)/(1+sinθ)
Ice Load (Fi):
Free body diagram. Forces acting on a concrete gravity dam
CVE 471 Water Resources Engineering 41/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d) Forces Acting on Gravity Dams Earthquake Force:
Fd = kWc
k: earthquake coefficient
Dynamic Force in the reservoir induced by earthquake
2 Fw = 0.726Ckγh1 θ′ C = 0.71− 90 Dynamic Force acting on a spillways ΣF = ρQ∆u
obtained using momentum equation Free body diagram. Forces acting on a concrete gravity dam
CVE 471 Water Resources Engineering 42/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d) Forces Acting on Gravity Dams
Wave Force may be considered for wide and long reservoirs.
Temperature Loads may be severe during construction because of hydration reactions
Free body diagram. Forces acting on a concrete gravity dam
CVE 471 Water Resources Engineering 43/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d) Stability Criteria
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 word, 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.
Floods (spring and summer) ÅÆ Ice load (winter).
No need to consider these two forces at the same time.
CVE 471 Water Resources Engineering 44/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d) 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
Forces in Usual Loading and earthquake forces
CVE 471 Water Resources Engineering 45/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d) Stability Criteria
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)
F.S0: Safety factor against overturning. F.Ss: Safety factor against sliding. F.Sss: Safety factor against shear and sliding. However, since each dam site has unique features, different safety factors may be derived considering the local condition. CVE 471 Water Resources Engineering 46/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d) Stability Criteria
The factor of safety against overturning:
M ∑ r where ΣM : total resisting moment about the toe. F.S0 = r ΣM : total overturning moment about the toe. ∑ M0 0
The factor of safety against sliding:
f V F.S = ∑ s ∑ H
where f: coefficient of friction between any two planes ΣV: vectorial summation of vertical forces. ΣH: vectorial summation of horizontal forces.
CVE 471 Water Resources Engineering 47/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d) Stability Criteria
The factor of safety against sliding and shear:
f ∑V + rAτ s F.S = (in the dam) ss ∑ H
f ∑V + cA F.S = (at foundation level) ss ∑ H
where A: Area of the shear plane,
τs: shear strength of concrete r: factor to express max allowable average shear stress r=0.33, 0.50, and 1.0 for usual, unusual, and extreme loading, respectively. f: coefficient of friction between any two planes ΣV: vectorial summation of vertical forces. ΣH: vectorial summation of horizontal forces.
CVE 471 Water Resources Engineering 48/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d) Stability Criteria
The contact stress between the foundation and the dam or the internal stress in the dam body must be compressive:
V Mc σ = ∑ ± A I
Normal stress Bending or flexural stress Base pressure distribution
where σ : vertical normal base pressure A: Area of the shear plane, M: net moment about the centerline of the base (M = ΣV.e) e: eccentricity (B / 2 − x ) c: B/2 I : Moment of inertia (B3/12) ΣV: vectorial summation of vertical forces.
CVE 471 Water Resources Engineering 49/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d) Stability Criteria
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 certain range of eccentricity.
ΣV Mc for a unit width ΣV ΣV ×e× B / 2 ΣV 6e σ = ± σ min = − = 1− ≥ 0 A I A B3 /12 B B
σmin ≥ 0 can be achieved if e ≤ B/6
Full reservoir Æ σmax at the downstream face
Empty reservoir Æ σmax at the upstream face
Base pressure distribution CVE 471 Water Resources Engineering 50/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d) 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.
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
CVE 471 Water Resources Engineering 51/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d) Stability Criteria
Concrete gravity dams have varying thickness.
Hence the inclined compressive stresses parallel to the face of the dam need to be computed.
For a concrete gravity dam with slopes of 1V:mH at the upstream face and 1V:nH at the down stream face, the major principle compressive stresses,
σiu (parallel to the upstream face) and σid (parallel to the downstream face) are obtained from the static equilibrium of forces in the vertical direction as:
(ΣFy=0)
where σu and σd vertical normal compressive stresses and pu and pd hydrostatic pressures CVE 471 Water Resources Engineering at the upstream and downstream faces, respectively. 52/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d) Stability Criteria
Internal horizontal and vertical shear stresses at the upstream and downstream faces are obtained by equating the total moment to zero
as (ΣMA=0, ΣMB=0):
where τhu, τhd, τvu, and τvd are the horizontal and vertical internal shear stresses at the upstream and downstream faces, respectively.
CVE 471 Water Resources Engineering 53/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d) Stability Criteria
The maximum compressive stress, σmax ,must be smaller than a certain fraction of the compressive strength of concrete, σc, and foundation material, σf.
Unconfined compressive strength, σf Safety criteria for concrete gravity dams for foundation materials
CVE 471 Water Resources Engineering 54/101 3. DAMS
Gravity Dams
Concrete Gravity Dams (cont’d) Stability Criteria
Excessive care must be taken during the filling of the reservoir.
Initially 1/3 of the dam height may be filled first.
After waiting for several weeks and assuring that the dam is safe, further filling is performed.
Since safety levels change with respect to upstream water depth, gravity dams must be analyzed for various operating levels and empty reservoir cases, separately.
For the empty reservoir case, the overturning tendency must be checked with respect to the toe and heel, separately.
The stability against sliding may be improved by providing a cut off wall in the foundation at the upstream side.
CVE 471 Water Resources Engineering 55/101 3. DAMS
Gravity Dams
Prestressed Concrete Gravity Dams In a prestress concrete dam, forces are applied to the dam before the reservoir is filled in order to counter undesirable stress that would develop in the absence of the prestressing forces. For prestressing, either small-diameter high-tensile wires or high- tensile steel bars can be used. Roller Compacted Concrete (RCC) Gravity Dams RCC dam is constructed using cement, water, fine and course aggregates, and fly ash which are mixed in certain proportions to have a no-slump, rather dry composition. Construction is based on the compaction of this mixture by heavy static or vibrating rollers. Construction period of RCC dams is shorter than that of conventional concrete gravity dams.
CVE 471 Water Resources Engineering 56/101 3. DAMS
Overview
Classification of Dams
Parts of Dams
Planning of Dams
Construction of Dams
Concrete Gravity Dams
Arch Dams
Buttress Dams
Embankment (Fill Dams)
Cross-sectional Layout Design of Dams
Local Scour at the Downstream of Dams
Dam Safety and Rehabilitation
CVE 471 Water Resources Engineering 57/101 3. DAMS
Arch Dams
Arch dams are thin concrete structures.
Gokcekaya, Oymapinar, Karakaya, Gezende, and Berke dams in Turkey.
Gokcekaya Dam Berke Dam Karakaya Dam
CVE 471 Water Resources Engineering 58/101 3. DAMS
Arch Dams
Arch dams: Oymapinar Dam, Turkey
CVE 471 Water Resources Engineering 59/101 3. DAMS
Arch Dams
Hoover Dam, USA CVE 471 Water Resources Engineering 60/101 3. DAMS
Arch Dams
Arch dams are thin concrete structures.
Stability of an arch dam is based on its self weight and its ability to transmit most of the imposed water loads into the valley walls.
At the sites of arch dams, the side formations and foundations should be very stiff to resist the applied load.
For effective arching action, the radius of the arch should be as small as possible.
They are formed by concrete blocks having base dimensions of approximately 15 m by 15 m and height of 1.5 m
Reinforcement is not generally required in thick arch dams because it increases the cost drastically.
Arch dams have normally higher structural safety than conventional gravity dams.
CVE 471 Water Resources Engineering 61/101 3. DAMS
Arch Dams
Types of Arch Dams
Arch dams are classified according to geometric characteristics of the valley where they are adopted.
Arch dams are classified according to the location of the center and magnitude of the central angle
Constant-center (variable angle) arch dams are suitable for medium-high dams in U-shape valleys. They have single curvature in plan with vertical upstream face.
CVE 471 Water Resources Engineering 62/101 3. DAMS
Arch Dams
Types of Arch Dams
Variable-center (constant angle) arch dams are suitable for V-shape valleys.
Radius of the arc reduces with respect to depth.
So arching action is more pronounced at low depths.
Since these types of dams are normally thinner than constant-center dams, they are more elastic and safer. Variable-center (constant angle) arch dams
CVE 471 Water Resources Engineering 63/101 3. DAMS
Arch Dams
Types of Arch Dams
Variable-center (variable angle) arch dams are composed of the combination of two types described above.
Load distribution in vertical direction governs the cross-sectional shape of the dam.
This type has a pronounced double Variable-center (variable angle) arch dams curvature
They utilized the concrete strength more compared the other types resulting in thinner and more efficient structure.
However, tensile stresses may develop in the dam body.
Gokcekaya Dam CVE 471 Water Resources Engineering 64/101 3. DAMS
Arch Dams
Types of Arch Dams
Variable-center (variable angle) arch dams
Gokcekaya Dam
Cross-section of Gokcekaya Dam CVE 471 Water Resources Engineering 65/101 3. DAMS
Arch Dams
Design of Arch Dams
Structural design of an arch dam requires the determination of load distribution in the dam body using the trial load method and applications of the theory of elasticity and the theory of shells.
Structural design is beyond the scope of this course.
Simplified design:
The determination of the thickness at any elevation of an arch dam whose crest elevation has already been determined in the hydrologic design step.
In the arch dams, the total load is shared by arch and cantilever actions and transmitted to the sides and foundation, respectively.
Therefore, the base width of arch dams is usually much narrower than that of concrete gravity dams having almost the same height.
Hence, the effect of uplift pressure can be ignored.
CVE 471 Water Resources Engineering 66/101 3. DAMS
Arch Dams
Design of Arch Dams
However, effect of temperature stresses should be checked to ensure that they are smaller than tensile strength.
Near the crest of the dam, most of the loads taken by arches and transmitted to the side abutments.
Near the bottom of the dam, cantilevers take most of the load and transmit to the foundation.
Gokcekaya Dam
CVE 471 Water Resources Engineering 67/101 3. DAMS
Arch Dams
Design of Arch Dams
In the following analysis, the water thrust induced by hydrostatic pressure is assumed to be taken by arch action only and transmitted to the sides.
The differential force acting on a differential element having a central angle of dΦ is
dFv= P r dΦ
The vertical component of this Free-body diagram for arch dam analysis force is
dF'v= P r dΦ sinΦ
CVE 471 Water Resources Engineering 68/101 3. DAMS
Arch Dams
Design of Arch Dams
Integration of this force along the arc length gives the total γ horizontal force, H . φ φ h γ π π θ π 2 γ a θa Hh = 2 hr sin d = −2 hrcos − cos − = 2 hr sin ∫ 2 2 2 2 − πa θ Free-body diagram for arch dam analysis 2 2
where h: the height of the arch rib relative to the reservoir surface r: the radius of arch
θa: the central angle
CVE 471 Water Resources Engineering 69/101 3. DAMS
Arch Dams
Design of Arch Dams
The equilibrium of forces in y- direction involves
Hh = 2Ry where θ a Ry = Rsin 2 Therefore γ 2 hr sinθ a = 2Rsin a 2 2 Free-body diagram for arch dam analysis θ R = γhr where R: the reaction offered by the sides against the transmission of water thrust.
As observed from the R = γhr, the reaction at the sides is directly proportional to the arc radius at a given height. Therefore, narrow valleys having stiff geological formations and small r-values are suitable for arch dams.
CVE 471 Water Resources Engineering 70/101 3. DAMS
Arch Dams
Design of Arch Dams
If the thickness of the arch rib, t, is relatively small as compared with r, there is small difference between the average and maximum compressive stresses in the rib and σ≈R/t.
The required thickness of the rib is then γhr t = (the thickness varies linearly with depth.) σ all
where
σall: the allowable working stress for concrete in compression.
CVE 471 Water Resources Engineering 71/101 3. DAMS
Arch Dams
Design of Arch Dams
The volume of concrete per unit height of a single arch rib across a
canyon of width of Ba is V=Lt
where L is the arch length which is equal to rθa (θa in radians).
Inserting the values of L and t into the equation above
γh 2 V = σ r θa all
CVE 471 Water Resources Engineering 72/101 3. DAMS
Arch Dams
Design of Arch Dams
The optimum central angle θa for a minimum volume of arch rib can be determined as 133º34‘ by differentiating V with respect to
θa and equating the result to zero.
This is the reason why a constant-angle arch dam can be design to require less concrete than a constant-center dam.
In practice, the central angles of arch dams vary from 100º to 140º.
However, the formwork of a constant-angle dam is more difficult.
CVE 471 Water Resources Engineering 73/101 3. DAMS
Arch Dams
Design of Arch Dams
The optimum central angle θa for a minimum volume of arch rib can be determined as 133º34‘ by differentiating V with respect to
θa and equating the result to zero.
This is the reason why a constant-angle arch dam can be design to require less concrete than a constant-center dam.
In practice, the central angles of arch dams vary from 100º to 140º.
However, the formwork of a constant-angle dam is more difficult.
CVE 471 Water Resources Engineering 74/101 3. DAMS
Overview
Classification of Dams
Parts of Dams
Planning of Dams
Construction of Dams
Concrete Gravity Dams
Arch Dams
Buttress Dams
Embankment (Fill Dams)
Cross-sectional Layout Design of Dams
Local Scour at the Downstream of Dams
Dam Safety and Rehabilitation
CVE 471 Water Resources Engineering 75/101 3. DAMS
Buttress Dams
A buttress dam consists of a sloping slab.
Depending on the orientation of slab, a buttress dam may be classified as
flat-slab buttress dam
multiple-arch buttress dam Elmali Dam construction, Istanbul, 1941
A typical buttress dam.
CVE 471 Water Resources Engineering Elmali Dam 76/101 3. DAMS
Buttress Dams
Flat-slab buttress dams
Lake Tahoe Dam, California, USA
CVE 471 Water Resources Engineering 77/101 3. DAMS
Buttress Dams
Multiple-arch buttress dams
Bartlett Dam , Phoenix, Arizona, USA
CVE 471 Water Resources Engineering 78/101 3. DAMS
Buttress Dams
Some advantages of buttress dams over conventional gravity dams:
They can be constructed on foundations having smaller bearing capacity then required for gravity dams.
Since they have thinner slabs, possibility of development of vertical cracks is less.
Problems encountered during the setting of concrete are reduced.
Unless a mat foundation is used, uplift forces are negligibly small because of hollow spaces provided between the buttresses.
Ice pressures are also small as the ice sheet slides up the inclined slab. Main disadvantage of buttress dams:
May have comparable costs, because of increased formwork and reinforcement . There is only one buttress dam in Turkey (Elmali 2 Dam). Elmali 2 Dam
CVE 471 Water Resources Engineering 79/101 3. DAMS
Overview
Classification of Dams
Parts of Dams
Planning of Dams
Construction of Dams
Concrete Gravity Dams
Arch Dams
Buttress Dams
Embankment (Fill Dams)
Cross-sectional Layout Design of Dams
Local Scour at the Downstream of Dams
Dam Safety and Rehabilitation
CVE 471 Water Resources Engineering 80/101 3. DAMS
Embankment (Fill) Dams
They composed of fill of suitable earth materials at the dam site.
Coarse-grained soils (gravel and coarse sand)
relatively pervious,
easily compacted,
resistant to moisture,
Clay is considered as a core material (impermeable)
unstable when saturated (expands due to wetting, hard to compact)
Therefore, clay mixed with sand and fine gravel is used as a core.
Core must be compacted in thinner layers with fairly accurate moisture control.
Compacted asphalt may also be used as an economical core material in case of loose foundations.
Asphalt can absorb earthquake shocks effectively.
CVE 471 Water Resources Engineering 81/101 3. DAMS
Embankment (Fill) Dams
Embankment dams are usually safer against deformations and settlements. Embankment dams Earth-fill dams Rock-fill dams (More than 50% of the total material is of rock.) Earth-fill dams in Turkey Seyhan Dam Demirkopru Dam Cubuk 2 Dam Bayindir Dam Rock-fill dams in Turkey Keban Dam Ataturk Dam Hasan Ugurlu Dam
Hasan Ugurlu Dam CVE 471 Water Resources Engineering 82/101 3. DAMS
Embankment (Fill) Dams
Body volume of embankment dams is relatively greater than the other types of dams.
Normally cheaper than the other types where there is enough fill material in the close vicinity.
Fill dams comprise more than 70% of the dams in the world and 90% in Turkey.
Keban Dam
CVE 471 Water Resources Engineering 83/101 3. DAMS
Embankment (Fill) Dams
Earth-fill Dams
Construction:
Placement of selected material on layers of 50 cm thick and compaction.
Non-organic and non-plastic soils are needed.
The embankment soil is usually irrigated at the borrow area.
Piezometers can be placed in the embankment at various depths during the construction to measure the pore water pressure.
A typical earth-fill dam is constructed in a multi-layer formation.
CVE 471 Water Resources Engineering 84/101 3. DAMS
Embankment (Fill) Dams
Earth-fill Dams
A typical earth-fill dam is constructed in a multi-layer formation.
Earth dam on pervious foundation CVE 471 Water Resources Engineering 85/101 3. DAMS
Embankment (Fill) Dams
Earth-fill Dams
Seepage through an earth-fill dam.
The flow rate, ∆q, between two flow lines can be expressed using the Darcy law as ∆h K: the hydraulic conductivity ∆q = KAi = K∆D i : the hydraulic gradient ∆L ∆h: head loss (h/N) The total flow rate, q N : number of equipotential drops Kh q = N′ N’: the number of stream tubes N CVE 471 Water Resources Engineering 86/101 3. DAMS
Embankment (Fill) Dams
Earth-fill Dams
Drainage systems in an earth-fill dam.
Chimney drains, in the embankment as well as enlarged toe drains are effective in controlling the seepage through the dam.
CVE 471 Water Resources Engineering 87/101 3. DAMS
Embankment (Fill) Dams
Rock-fill Dams
Having relatively high pore space
Can be adopted to weaker foundations where a gravity dam cannot be constructed.
Cross-sections of typical rock-fill dams
CVE 471 Water Resources Engineering 88/101 3. DAMS
Embankment (Fill) Dams
Rock-fill Dams (Ataturk Dam)
Largest dam in Turkey
Reservoir Volume: 48.7 x 109 m3
Installed capacity: 2400 MW
Annual energy production: 8.9 x 109kWh
Irrigated land: 874200 ha (with the completion of the project)
A cross-sections of the Ataturk Dam
CVE 471 Water Resources Engineering 89/101 3. DAMS
Embankment (Fill) Dams
Rock-fill Dams (Ataturk Dam)
A cross-sections of the Ataturk Dam
CVE 471 Water Resources Engineering 90/101 3. DAMS
Overview
Classification of Dams
Parts of Dams
Planning of Dams
Construction of Dams
Concrete Gravity Dams
Arch Dams
Buttress Dams
Embankment (Fill Dams)
Cross-sectional Layout Design of Dams
Local Scour at the Downstream of Dams
Dam Safety and Rehabilitation
CVE 471 Water Resources Engineering 91/101 3. DAMS
Cross-sectional Layout Design of Dams
A suitable dam cross-section should be provided such that both safety and desired functionality concerning service requirement are attained.
Sufficient crest width, tc must be provided. a width of two lane traffic may be selected.
For small embankment dams
up to Hf=15 m.
tc=0.2Hf+3 For large embankment dams
up to Hf=150 m. 1/3 tc=3.6 (Hf )
where tc and Hf are in meter.
CVE 471 Water Resources Engineering 92/101 3. DAMS
Cross-sectional Layout Design of Dams
By examining some existing muti-purpose concrete gravity dams throughout the world, Yanmaz et al. (1999) proposed the following regression equations to define the shape of a gravity dam.
* H =0.1075 Ht
tc=0.0475 Ht +2.392
where all variables are in meter
CVE 471 Water Resources Engineering 93/101 3. DAMS
Cross-sectional Layout Design of Dams
United States Bureau of Reclamation (USBR) propose the following formulas for cross-sectional layout of arch dams:
tc = 0.01(Ht +1.2Ba ) H / 400 H t 3 t All the dimensions are in ft tb = 0.0012Ht Ba B0.15 400 t = 0.95t 0.45Ht b
where Ba: the span width at the crest
B0.15: the span width at 15% of the dam height above the base
t0.45Ht: the dam thickness at 45% of the dam height above the base.
CVE 471 Water Resources Engineering 94/101 3. DAMS
Cross-sectional Layout Design of Dams
The crest elevation of a dam is to be determined such that there is almost no overtopping danger of the flood wave during the occurance of the design flood. Freeboards on flood levels for concrete and embankment dams
Greater freeboards are required for embankment dams since they are susceptible to erosion at the downstream face due to overtopping from their crest.
The required side slopes of concrete gravity dams are determined from stability analyses.
The maximum downstream slope of gravity dams is 45°.
Side slopes of embankment dams are determined on the basis of seepage and slope stability analyses.
CVE 471 Water Resources Engineering 95/101 3. DAMS
Overview
Classification of Dams
Parts of Dams
Planning of Dams
Construction of Dams
Concrete Gravity Dams
Arch Dams
Buttress Dams
Embankment (Fill Dams)
Cross-sectional Layout Design of Dams
Local Scour at the Downstream of Dams
Dam Safety and Rehabilitation
CVE 471 Water Resources Engineering 96/101 3. DAMS
Local Scour at the Downstream of Dams
Excessive kinetic energy of the flowing water at the downstream of outlet works (spillways, sluiceways etc.) should be dissipated in order to prevent the erosion of the streambed and the banks below the dam.
Local scour at the downstream of the dam and sluice gates
Excessive scours at the downstream of Keban Dam have resulted in serious foundation stability problems (depth of approx 30 m).
CVE 471 Water Resources Engineering 97/101 3. DAMS
Local Scour at the Downstream of Dams
Some of the scour prediction equations are given in the table.
Scour prediction equations for the downstream of dams. ds: the maximum depth of scour hole in m.
b: the thickness of the jet in m.
Φ: the side inclination for the scour hole,
Fr: Jet Froude number.
U: the velocity of the jet in m/s
∆=(γs- γ)/γ, 3 γs: : specific weight of sediment in kN/m γ : specific weight of water in kN/m3.
Wf: Fall velocity in m/s
q: unit discharge in m3/s/m
Hg: gross head in m
h: tailwater depth in m
D50: median size of bed material in m. CVE 471 Water Resources Engineering 98/101 3. DAMS
Overview
Classification of Dams
Parts of Dams
Planning of Dams
Construction of Dams
Concrete Gravity Dams
Arch Dams
Buttress Dams
Embankment (Fill Dams)
Cross-sectional Layout Design of Dams
Local Scour at the Downstream of Dams
Dam Safety and Rehabilitation
CVE 471 Water Resources Engineering 99/101 3. DAMS
Dam Safety and Rehabilitation
Excessive care must be taken in planning, design, and construction stages of a dam.
Major causes for a dam break:
Inadequate spillway capacity,
Improper construction of any type of dam,
Insufficient compaction of embankment dams or compaction with undesirable water content,
Improper protective measures,
Excessive settlements, etc
Continuous inspection and monitoring are required to assess the safety level of the dam throughout the lifetime.
CVE 471 Water Resources Engineering 100/101 3. DAMS
Dam Safety and Rehabilitation
Upon periodic inspection, the following deficiencies may be observed that are indicators of problems:
Large horizontal and vertical movements of crest,
Tilting of the roadway along the crest,
Deformation of embankment slope,
Higher than usual pore water pressure in embankment dams,
Unusual seepage at the toe or edges of an embankment dam,
Seepage flows with not decreasing with low flow conditions,
Turbit outflow through the embankment,
Tilting of the spillway crest
Increased leakage into inspection galleries in concrete dams, etc.
CVE 471 Water Resources Engineering 101/101