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 hold
and control the flow of water for uses such as drinking water
supplies, irrigation, flood control and hydropower generation
etc.
3

WHAT IS A DAM?
4
http://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 river
downstream from the dam
• Loss of flowing water habitat and replacement with standing
water (reservoir) habitat
• Interruption of animal movements along the course of the river
• Possible alteration of the fish community in the region of the
river
• Interruption of genetic exchange among populations inhabiting
the river course
• Reduction in the delivery of river nutrients to downstream
section of the river because of entrapment by the reservoir
• The loss of the floodplain habitat and connectivity between the
river and bordering habitats upland
8

PURPOSE DISTRIBUTION OF DAMS
Source: International Commission on Large Dams (ICOLD)
http://www.icold-cigb.net
9

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
11

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
12

TYPES OF STORAGE DAMS
(1). Embankment Dams: Constructed of earth-fill and/or rock-fill.
Upstream and downstream face slopes are similar and of
moderate angle, giving a wide selection and high construction
volume relative to height.
(2). Gravity Dams: Constructed of mass concrete. Face slopes are
dissimilar, generally steep downstream and near vertical upstream
and dams have relatively slender profiles depending upon type
Note: Embankment dams are numerically dominant for technical and
economical reasons, and account for over 85-90% of all dams built
13

Concrete Dams
• Gravity Dam
These dams resist the horizontal
thrust of the water entirely by their
own weight. These are typically
used to block streams through
narrow gorges.
• Buttress Dam
In these dams, the face is held up
by a series of supports. It can
take many forms -- the face may
be flat or curved.
• Arch Dam
It is a curved dam which is
dependent upon arch action for its
strength. Arch dams are thinner
and therefore require less
material than any other type of
dam.
Embankment Dams
Earth-fill Dam
These, also called earthen,
rolled-earth or simply earth
dams, are constructed as a
simple embankment of well
compacted earth.
Rock-fill Dam
These are embankments of
compacted free-draining
granular earth with an
impervious zone. The earth
utilized often contains a large
percentage of large particles
hence the term rock-fill is
used.
14

Embankment dam
Gravity dam
Arch damButtress dam
15

TYPES OF DAMS
http://www.icold-cigb.net/
18

Following are the important factors considered for the selection of site
for 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
19

The choice of dam is decided upon by examining foundation conditions,
load strains, temperature and pressure changes, chemical
characteristics of ground water and possible seismic activity.
The followings important factors are considered for the selection of type
of 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
20

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.
21

STAGES FOR DAM SITE APPRAISAL
24
24

ANCILLARY WORKS
Dams require certain ancillary structures and facilities to enable
them to discharge their operational function safely and effectively.
In particular, adequate provision must be made for the safe
passage of extreme floods and for controlled draw-off and
discharge of water in fulfillment of the purpose of the reservoir.
Spillways, outlets and ancillary facilities are incorporated as
necessary 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 water
safely downstream when the reservoir is full.
The Spillways can be
Uncontrolled (Normally)
Controlled
Note: Concrete dams normally incorporate an over-fall or
crest spillway, but embankment dams generally require a
separate side-channel or shaft spillway structure located
adjacent to the dam.
27

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
29

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
30

SIDE CHANNEL SPILLWAYS
Spillway in which flow, after passing over the crest, is carried away in
a channel running parallel to the crest
* used in narrow canyons in which there is sufficient crest length
for overflow or chute is available
31

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 trash
racks protect inlet
32

SIPHON SPILLWAY
Siphon PrincipleTypical Siphon Spillway
Air vent used automatically maintain the water-surface elevation
large 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
33

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)
34

SPILLWAY, OUTLETS AND ANCILLARY WORKS
Outlet Works:
Controlled outlets are required
to permit water to be drawn off
as is operationally necessary.
Provision must be made to
accommodate the required
penstocks and pipe works with
their associated control gates
or valves.
35

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 construction
and subsequently employed as a discharge facility for the completed
dam.
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
36

Internal Drainage:
Seepage is always present within the body of dam. Seepage flows
and their resultant internal pressures must be directed and
controlled.
In embankment dams, seepage is effected by suitably located
pervious zones leading to horizontal blanket drains or outlets at
base level
In concrete dams vertical drains are formed inside the upstream
face, and seepage is relieved into an internal gallery or outlet drain.
In arch dams, seepage pressure in rock abutments are frequently
drained by purpose built system of drainage ducts
37

The tunnels inside the dam for control of seepage and monitoring structural stability
Seepage Control in Concrete Dams
38

Internal Galleries and Shafts
Galleries and shafts are provided as means of allowing internal
inspection, particularly in concrete dams.
These can be used to accommodate structural monitoring and
surveillance 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)
40

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.
41

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.
42

FORCES ON DAMS
Secondary 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 rock
mass ( This is of particular concern to arch and cupola dams)
43

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.
44

LOAD COMBINATION
A dam is designed for the most adverse combinations of loads as they
have 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 water
conditions, normal uplifts and silt load
For flood discharge conditions: reservoir at max flood level, all
spillway gates open, tail water at flood levels, normal uplifts and silt
load
45

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.
46

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
49

(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

(A) PRIMARY LOADS
• 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.
51

(A) PRIMARY LOADS
• 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
52

(A) PRIMARY LOADS
• 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
53

(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.
54

(B) SECONDAY LOADS
• 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

(B) SECONDAY LOADS
• 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

(B) SECONDAY LOADS
• THERMAL AND DAM–FOUNDATION INTERACTION EFFECTS
• Beyond the scope of our course and comprehensively discussed in
USBR (1976).
57

(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.
61

• 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 they
have 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 water
conditions, normal uplifts and silt load
For flood discharge conditions: reservoir at max flood level, all
spillway gates open, tail water at flood levels, normal uplifts and silt
load
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

with regard to
• 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 Moment
FOS
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 tanϕ
represents frictional resistance to shearing, where is the angle of
shearing resistance or of sliding friction,
68

69

70

• 2. translation and sliding
71

• CRITERIA AND
PRINCIPLES
• 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 Moment
FOS
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
2253051
2
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
1000/24005075
2
1
2
=
×××=
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 drainage
galleries is represented by dash line.
However, the drainage galleries
control the pressure distribution and
in present problem, the uplift
pressure at drainage gallery is given
as 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 is
taken equal to heal of water. i.e., γwh
Γwx80.
While at the drainage gallery it is
50% of γwx80. i.e., γwx40
And at the toe it becomes zero as
there 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

with regard to
• ii. Shear friction factor, FSF;
• iii. Limit equilibrium factor, FLE.
95

1. Stability against Rotation and Overturning
momentgOverturnin
momentgStabilizin
FOS =
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
WW
FOS
wh
It ranges from 1.5~2.5
96

2. Stability against sliding of dam
59.0
2.5359/3200
=
=
=
∑
∑
FOS
FOS
V
H
FSS
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
S
F
φ
It ranges from 1.0 (extreme) ~ 3.0 (normal)
ii. Shear Friction Factor, FSF:
Foundation condition: Inferior
condition with limestone
tanΦ=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).
10
0

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
M
xwherex
B
e ,,
2
ton.
-.-
-UWW
V
25359
1560224194500
21
forcesverticalTotal
=
=
+=
=∑
mton
P
UU-U
WW
M
−=
×−
×−×−×
×+×=
=∑
4.133183
67.26
36333.592581
33.332561
at toemomentTotal
position of resultant
mx 85.24
2.5359
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
M
xwherex
B
e ,,
2
mx 85.24
2.5359
4.133183
==
3
B
m
B
33.10
3
=
3
B
m
x
B
e
15.6
85.24
2
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*6
1
62
2.5359
6
1
/89.137
62
15.6*6
1
62
2.5359
6
1
mton
B
e
B
V
P
mton
B
e
B
V
P
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 compression
103

(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
2
1
22
1
=
=
=
+=
−+=
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

Chapter 6 concrete dam engineering with examples

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