Chapter 6 concrete dam engineering with examples

Concrete dam engineering with examples

1. CHAPTER 6: CONCRETE DAM 
ENGINEERING
1
0401544 -HYDRAULIC STRUCTURES
University of Sharjah
Dept. of Civil and Env. Engg.
DR. MOHSIN SIDDIQUE
ASSISTANT PROFESSOR

2. 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 select ion
(2). Understand the role of ancillary works in the dam
(3). Identify and estimate the various forces actin g on the dam
(4). Perform both static and dynamic analysis as pa rt of design process
2
Reference: Novak, P., Moffat, I.B. and Nalluri, Hydraulic structure s, 4th ed

3. WHAT IS A DAM? C
A damis 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

4. WHAT IS A DAM?
4
http://www.fs.fed.us/eng/pubs/htmlpubs/htm12732805/longdesc/fig01ld.htm

5. 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

6. WHAT IS A DAM?
6
Tygart River Dam

7. BENEFITS OF DAMS
C
The benefits of dams are usually to the advantage of humans. T hey
may include:
H
Irrigation
H
Hydro-electric production
H
Flood control
H
Recreational opportunities
H
Navigation
H
Industrial and Domestic water supply
H
Aeration of water
C
For animals the benefits may include:
H
Larger numbers of fish and birds in the reservoir
H
Greater habitat diversity
7

8. DISADVANTAGES OF DAMS ImpactsonEnvironmentalandEcosystemofthearea
•
Changes in temperature and flow/sediment transport in the r iver
downstreamfromthe dam
•
Loss of flowing water habitat and replacement with standing
water (reservoir) habitat
•
Interruption of animal movements along the course of the riv er
•
Possible alteration of the fish community in the region of th e
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

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

10. PURPOSE DISTRIBUTION OF DAMS
Source: International Commission on Large Dams (ICOLD)
http://www.icold-cigb.net/
10

11. CLASSIFICATION OF DAMS: Dams are classified on several aspects, some of the important aspects
are as follow:
1)
Based on Hydraulic Design:
A
Over flow dams (e.g. concrete dams)
A
Non over flow dams (e.g. embankment dams)
2)
Based on Structural Design:
A
Gravity dams
A
Arch dams
A
Buttress dams
3)
Based on Usage of Dam:
A
Storage dams
A
Diversion dams
A
Detention dams
11

12. CLASSIFICATION OF DAMS: 4)
Based on Construction Material:
A
Concrete / Masonary dams
A
Earthfill dams
A
Rockfill dams
A
Earth and rockfill dams
A
Concrete faced rockfill dams (CFRD)
5)
Based on Capacity:
A
Small dams
A
Medium dams
A
Large dams
12

13. TYPES OF STORAGE DAMS (1). Embankment Dams:Constructed of earth-fill and/or rock-fill.
Upstreamand downstreamface 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 downstreamand near vertical upstream
and dams have relatively slender profiles depending upon ty pe
Note: Embankment dams are numerically dominant for technical and
economical reasons, and account for over 85-90% of all dams built
13

14. TYPES OF STORAGE DAMS
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 damwhich is
dependent upon arch action for its
strength. Arch dams are thinner
and therefore require less
material than any other type of
dam.
C
Embankment Dams
H
Earth-fill Dam
C
These, also called earthen,
rolled-earth or simply earth
dams, are constructed as a
simple embankment of well
compacted earth.
H
Rock-fill Dam
H
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 termrock-fillis
used.
14

15. TYPES OF STORAGE DAMS
Embankment dam
Gravity dam
Arch dam
Buttress dam
15

16. 16

17. 17

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

19. Following are the important factors considered for the sele ction 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

20. The choice of damis decided upon by examining foundation conditions,
load strains, temperature and pressure changes, chemical
characteristics of ground water and possible seismic activ ity.
The followings important factors are considered for the sel ection of type
of dams:
SELECTION OF DAM TYPE 1) Topography
2)
Geology and nature of foundation
A
Bearing capacity of the underlying soil
A
Foundation settlements
A
Permeability of the foundation soil
A
Foundation excavation
3) Hydraulic Gradient
4)
Availability of construction materials
5)
Economics
20

21. 6) Spillway location
7) Safetyconsiderations
8) Earthquakezones
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

22. 22

23. 23

24. STAGES FOR DAM SITE APPRAISAL
24
24

25. ANCILLARY WORKS
25

26. ANCILLARY WORKS
PDams require certain ancillary structures and facilities t o enable
themto discharge their operational function safely and effecti vely.
PIn 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 reser voir.
PSpillways, outlets and ancillary facilities are incorporated as
necessary for the purpose of the damand appropriate to its type.
Ancillary works includes construction of spillways,
stilling basins, culverts or tunnels for outlet wor ks, valve
towers etc. It also include crest details e.g., roa dway,
drainage works, wave walls etc.
26

27. SPILLWAYS TSpillways:The purpose of spillway is to pass flood water
safely downstreamwhen the reservoir is full.
T
The Spillways can be
T
Uncontrolled (Normally)
T
Controlled
TNote:
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

28. 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

29. OVERFLOW SPILLWAYS
Section of a dam that allows water to pass over its crest widely
used on gravity, arch, & buttress dam
29

30. 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

31. 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

32. 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

33. SIPHON SPILLWAY
Siphon Principle
Typical 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

34. 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

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

36. SPILLWAYS, OUTLETS AND ANCILLARY WORKS ERiverDiversion:
E
Necessary to permit construction to proceed in dry conditio ns
E
An outlet tunnel may be adapted to this purpose during constr uction
and subsequently employed as a discharge facility for the co mpleted
dam.
E
Alternate of such tunnels can be coffer dams.
ECut-offs:
E
Used to control seepage around and under the flank of dams.
E
Embankment cut-offs are generally formed by
E
Wide trenches backfilled with rolled clay,
E
Grouting to greater depths
E
Grout Screen cut-offs in rock foundations
36

37. SPILLWAYS, OUTLETS AND ANCILLARY WORKS EInternalDrainage:
E
Seepage is always present within the body of dam. Seepage flows
and their resultant internal pressures must be directed and
controlled.
E
In embankment dams, seepage is effected by suitably located
pervious zones leading to horizontal blanket drains or outl ets at
base level
E
In concrete dams vertical drains are formed inside the upstr eam
face, and seepage is relieved into an internal gallery or out let drain.
E
In arch dams, seepage pressure in rock abutments are frequently
drained by purpose built systemof drainage ducts
37

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

39. SPILLWAYS, OUTLETS AND ANCILLARY WORKS EInternalGalleriesandShafts
EGalleries and shafts are provided as means of allowing internal
inspection, particularly in concrete dams.
EThese can be used to accommodate structural monitoring and
surveillance purpose.
Internal gallery at concrete-gravity dam inspected by D'Appolonia.
39

40. 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, a re 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 o f occurrence.
(e.g. tectonic effects, or the inertial loads assoc iated with seismic
activity)
40

41. 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

42. FORCES ON DAMS PrimaryLoads: (a): Water Load:This is a hydrostatic distribution of pressure with
horizontal resultant force P
1
. (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 simpl e elastic analysis the
resultant, P
2
, 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 discontin uities, with resultant
vertical loads identified as internal and external uplift, P
3
and P
4
,
respectively.
42

43. FORCES ON DAMS Secondary Loads: (a): Sediment load: Accumulated silt etc. generates a horizontal thrust,
considered as an equivalent additional hydrostatic load w ith horizontal
resultant P
5.
(b): Hydrodynamic wave load:This is a transient and random local load,
P
6, generated by wave action against the dam (not normall y significant).
(c): Ice Load:Ice thrust, P
7, from thermal effects and wind drag, may
develop in more extreme climatic conditions (not normall y significant).
(d): Thermal Load:(concrete dams), This is an internal load generated by
temperature differentials associated with changes in ambi ent conditions and
with cement hydration and cooling (not shown).
(e): Interactive effect:Internal, arising from relative stiffness and differenti al
deformations of dam and attributable to local variatio ns 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

44. FORCES ON DAMS ExceptionalLoad: (a): Seismic Load:Oscillatory horizontal and vertical inertia loads
are generated with respect to the dam and the retai ned 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, P
8
, is shown
(b): Tectonic Loads:Saturation, or disturbance following deep
excavation in rock, may generate loading as a resul t of slow tectonic
movements.
44

45. LOAD COMBINATION A damis designed for the most adverse combinations of loads as the y
have reasonable probability of simultaneous occurrence.
For construction conditions:Damis 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
i.With earthquake forces
ii.Without earthquake forces
For flood discharge conditions:reservoir at max flood level, all
spillway gates open, tail water at flood levels, normal upli fts and silt
load
45

46. 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 stabil ity. Both must be
satisfied with respect to the profile above all hor izontal planes within
the dam and the foundation. The overstress criterio n, 3, must be
satisfied for the dam concrete and for the rock fou ndation.
• The sliding stability criterion, 2, is generally t he most critical of the
three, notably when applied to the natural rock fou ndation.
46

47. 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

48. 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 structure s, 4
th
ed

49. GRAVITY DAM: LOADING CONCEPTS
Fig. Gravity dam loading diagram.
DFL=Design flood level;
NML=Normal maximum level, i.e. maximum retention level of spil l weir;
TWL=Tailwater level
49

50. GRAVITY DAM: LOADING CONCEPTS (A) PRIMARY LOADS
•WATER LOAD
• The external hydrostatic
pressure,
P
w
, at depth
z
1
is
expressed as
• where
γ
w
is the unit weight of
water, 9.81kN/m
3
• The
resultant horizontal force,
P
wh
, is determined as
• acting at height
z
1
/3
above
plane X–X.
A
resultant vertical force P
wv
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
P
wh’ and P
wv’
at d/s operative above
the toe, can also be calculated.
50

51. GRAVITY DAM: LOADING CONCEPTS (A) PRIMARY LOADS
•SELF LOAD
• Self-weight of structure is
accounted for in terms of its
resultant,
P
m
, which is
considered to act through the
centroid of the cross-sectional
area
A
p
of the dam profile
•γ
c
is the unit weight of
concrete, assumed as
23.5kN/m
3
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
P
m
and
the position of its line of action.
51

52. GRAVITY DAM: LOADING CONCEPTS (A) PRIMARY LOADS •SEEPAGE AND UPLIFT LOAD: Uplift load,
P
u
, is represented by the
resultant effective vertical components of intersti tial water pressure
u
w
.
• Uplift pressure at u/s=
γ
w
z
1
and uplift pressure at d/s
γ
w
z
2
52

53. GRAVITY DAM: LOADING CONCEPTS (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.
• P
u
acts through the centroid of
the pressure distribution
diagram at distance
y
1
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, z
d, can be
expressed as
53

54. GRAVITY DAM: LOADING CONCEPTS (B) SECONDAY LOADS
•SEDIMENT LOAD
• The magnitude of sediment
load,
P
s
, is given by
•Where,
z
3
issediment depth,
γs’
is the submerged unit
weight of sediment and the
K
a
is the active lateral pressure
coefficient and
ϕ
s
is the angle
of shearing resistance of the
sediment
•P
s
is active at
z
3
/3
above
plane X–X.
54

55. GRAVITY DAM: LOADING CONCEPTS (B) SECONDAY LOADS •HYDRODYNAMIC WAVE
LOAD
• It is considered only in
exceptional cases.
P
wave
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

56. GRAVITY DAM: LOADING CONCEPTS (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:
•
P
ice
=145kN/m
2
if ice
thicknesses > 0.6 m
•P
ice
=0 if ice thickness < 0.4m
56

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

58. 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. T hey 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 sele cted 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

59. GRAVITY DAM: LOADING CONCEPTS (C) EXCEPTIONAL LOADS
•SEISMICITY AND SEISMIC LOAD: PSEUDOSTATIC ANALYSIS
•INERTIA FORCES: MASS OF DAM
• Pseudostatic inertia and hydrodynamic loads are determined from
seismic coefficients
α
h
and
α
v
as detailed below.
• As with self-weight load,
P
m
, inertia forces are considered to operate
through the centroid of the dam section. The revers ible direction of the
forces will be noted; positive is used here to deno te inertia forces
operative in an upstream and/or a downward sense
59

60. GRAVITY DAM: LOADING CONCEPTS (C) EXCEPTIONAL LOADS
•SEISMICITY AND SEISMIC LOAD: PSEUDOSTATIC ANALYSIS
•HYDRODYNAMIC INERTIA FORCES: WATER REACTION.
• An initial estimate of these forces can be obtaine d using a parabolic
approximation to the theoretical pressure distribut ion as analyzed in
Westergaard (1933).
• Relative to any elevation at depth
z
1
below the water surface,
hydrodynamic pressure
p
ewh
is determined by
• In this expression
z
max
is the maximum depth of water at the section of
dam considered.
C
e
is a dimensionless pressure factor, and is a
function of
z
1
/z
ma
x
and
ϕ
u
,
the angle of inclination of the upstream face
to the vertical.
• The resultant hydrodynamic load is given by:
• and acts at elevation
0.40z
1
above X–X.
60
Check the formula !!

61. GRAVITY DAM: LOADING CONCEPTS (C) EXCEPTIONAL LOADS
•SEISMICITY AND SEISMIC LOAD: PSEUDOSTATIC ANALYSIS
•HYDRODYNAMIC INERTIA FORCES: WATER REACTION.
• Indicative values of C
e
are given in Table.
• As an initial coarse approximation, hydrodynamic l oad P
ewh
is
sometimes equated to a 50% increase in the inertia load, P
emh
.
61

62. •SEISMICITY AND SEISMIC LOAD: PSEUDOSTATIC ANALYSIS
•HYDRODYNAMIC INERTIA FORCES: WATER REACTION.
•Zanger Formula
GRAVITY DAM: LOADING CONCEPTS (C) EXCEPTIONAL LOADS

63. GRAVITY DAM: LOADING CONCEPTS (C) EXCEPTIONAL LOADS
•SEISMICITY AND SEISMIC LOAD: PSEUDOSTATIC ANALYSIS
•HYDRODYNAMIC INERTIA FORCES: WATER REACTION.
• The resultant vertical hydrodynamic load,
P
ewv
, effective above an
upstream face batter or flare may be accounted for by application of
the appropriate seismic coefficient to vertical wat er load,
P
wv
. 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 natu re.
63

64. LOAD COMBINATIONS A damis designed for the most adverse combinations of loads as the y
have reasonable probability of simultaneous occurrence.
For construction conditions:Damis 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
i.With earthquake forces
ii.Without earthquake forces
For flood discharge conditions:reservoir at max flood level, all
spillway gates open, tail water at flood levels, normal upli fts and silt
load
64

65. 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

66. 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 stabil ity. Both must be
satisfied with respect to the profile above all hor izontal planes within
the dam and the foundation. The overstress criterio n, 3, must be
satisfied for the dam concrete and for the rock fou ndation.
• The sliding stability criterion, 2, is generally t he most critical of the
three, notably when applied to the natural rock fou ndation.
66

67. GRAVITY DAM ANALYSIS •CRITERIA AND PRINCIPLES •1. Rotation and overturning,
Stabilizing Moment
FOS
Overturning Moment
∑
=
∑
67
These moments are calculated
at toe of the dam

68. GRAVITY DAM ANALYSIS •CRITERIA AND PRINCIPLES •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, F
SS
;
• ii. Shear friction factor, F
SF
;
• iii. Limit equilibrium factor, F
LE
.
• The resistance to sliding or shearing, which can b e 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 co efficient
tanϕ
represents frictional resistance to shearing, where is the angle of
shearing resistance or of sliding friction,
68

69. GRAVITY DAM ANALYSIS •CRITERIA AND PRINCIPLES •2. Translation and sliding
69

70. GRAVITY DAM ANALYSIS •CRITERIA AND PRINCIPLES • 2. Translation and sliding
70

71. GRAVITY DAM ANALYSIS •CRITERIA AND PRINCIPLES • 2. translation and sliding
71

72. GRAVITY DAM ANALYSIS •CRITERIA AND
PRINCIPLES
•2. Translation and sliding
•i. Sliding factor, FSS;
• For plane surface
• For inclined surface at a
small angle ,
Applied to well-constructed mass concrete, F
SSon a horizontal plane
should not be permitted to exceed 0.75 for the specifie d normal load
combination. F
SSmay be permitted to rise to 0.9 under the extreme
load combination.
72

73. GRAVITY DAM ANALYSIS
•CRITERIA AND PRINCIPLES •2. Translation and sliding
•ii. Shear Friction Factor, F
SF
:
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
A
h
is the thickness, T,
for a two-dimensional
section).i,e.,
A
h
=T
73

74. GRAVITY DAM ANALYSIS •CRITERIA AND PRINCIPLES •2. Translation and sliding
•ii. Shear Friction Factor,
• In some circumstances it may
be appropriate to include
downstream passive wedge
resistance,
P
p
,
as a further
component of the total
resistance to sliding which can
be mobilized.
W
W
is the weight of the passive wedge
74

75. GRAVITY DAM ANALYSIS •CRITERIA AND PRINCIPLES •2. Translation and sliding
•ii. Shear Friction Factor,
75

76. GRAVITY DAM ANALYSIS •CRITERIA AND PRINCIPLES •2. Translation and sliding
•iii. Limit Equilibrium Factor, F
LE:
It is the ratio of shear strength to
mean applied shear stress across a plane:
• Note that for the case of a horizontal sliding pla ne (α=0), equation
simplifies to the expression given for F
SF
, i.e. F
LE
=F
SF
(α=0).
• Recommended F
LE
=2.0 in normal operation, i.e. with static load
maxima applied, and F
LE
=1.3 under transient load conditions
embracing seismic activity.
76

77. GRAVITY DAM ANALYSIS •CRITERIA AND PRINCIPLES •2. Translation and sliding • It must be stressed that values for F
SS
, F
SF
and F
LE
cannot be directly
correlated.
• The stability factor and sliding criteria most app ropriate to a specific
dam are determined by the designer’s understanding of the
conditions
77

78. GRAVITY DAM ANALYSIS •CRITERIA AND PRINCIPLES •3. Overstress and material failure.
• The primary stresses determined in a comprehensive analysis by
the gravity method are as follows:
•
1. vertical normal stresses, σ
z
, on horizontal planes;
•
2. horizontal and vertical shear stresses, σ
zy
and σ
yz
;
•
3. horizontal normal stress, τ
y
, on vertical planes;
•
4. major and minor principal stresses, σ
1
and σ
3
(direction and
magnitude).
78

79. GRAVITY DAM ANALYSIS •CRITERIA AND PRINCIPLES •3. Overstress and material failure.
79

80. GRAVITY DAM ANALYSIS •CRITERIA AND PRINCIPLES •3. Overstress and material failure.
•(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

81. GRAVITY DAM ANALYSIS •CRITERIA AND PRINCIPLES •3. Overstress and material failure.
•(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

82. GRAVITY DAM ANALYSIS •CRITERIA AND PRINCIPLES •3. Overstress and material failure.
•(c) Horizontal normal stresses
82

83. GRAVITY DAM ANALYSIS •CRITERIA AND PRINCIPLES •3. Overstress and material failure.
•(d) Principal stresses
• The boundary values for σ
1
and σ
3
are
then determined as follows
83

84. GRAVITY DAM ANALYSIS •CRITERIA AND PRINCIPLES •3. Overstress and material failure.
84

85. 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

86. PROBLEM: A concrete gravity dam has the following dimensions:
EMax water level = 305 m
EBed level of river = 225 m
ECrest level = 309 m
ED/S face slope starts at 300 m
ED/S Slope= 2:3
EC/L of drainage galleries at 8m d/s of u/s face
EUplift pressures:
at Heal = 100 %
at Toe = 0 %
at drainage gallery = 50 %
86

87. PROBLEM: EDensity of concrete = 2400 kg/m
3
ENo tail water
EFoundation condition: inferior condition with limestone
EConsider self weight, hydrostatic pressure and uplift pressure
Check the stability of damfor
•1. Rotation and overturning,
•2. Translation and sliding and
•3. Overstress and material failure.
87

88. SOLUTION
CH
α
PTERH
PTTRH
 6:RPTORH
2
3
D6:6RNNORH
Wc
88

89.
α
m
m
m
2
3

Determine width of crest, Wc=?
m
Wc
Wc
12 16.9
84 225 309
Dam of Height
≈ =
= − =
=
80m
84m
75m
12m
heal
toe 89

90.
α
m
m
m
2
3

WATER LOAD
80m
84m
1/3*80=26.67m
75m
50m 12m
Pwh
12m
56m
heal
toe
( )
tons
h P
m ton h p
w wh
w w
3200
225 305 1
2
1
2/
/ 80 )80(1
2
2
2
=
− ×× =
=
= = =
γ
γ
3 3
/ 1 / 1000m mton m kg
w
= =
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

91.
α
m
m
m
2
3

SELF LOAD
80m
84m
75m
50m 12m
W1
W2
tons
W
2. 2419
1000 / 2400 84 12 1
=×
×
=
12m
56m
heal
toe
Acting 56m from toe
tons
W
4500
1000 / 2400 50 75
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
tons W W P
m
2. 6919 4500 2. 2419 2 1
=
+
=
+
=
91

92.
α
m
m
m
2
3

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
50m 12m
W1
W2
Pwh
12m
heal
toe
Without drainage galleries
With drainage
galleries
100%=γ
wh 50%=0.5γ
wh
SEEPAGE AND UPLIFT LOAD The uplift pressure at the heal is
taken equal to heal of water. i.e.,γ
wh
Γ
wx80.
While at the drainage gallery it is
50% ofγ
wx80. i.e.,γ
wx40
And at the toe it becomes zero as
there is no tail water.
where
h=80m
γ
w=1000kg/m
3
=1mton/m
3
92

93.
α
m
m
m
2
3

80m
84m
1/3*80=26.67m
75m
50m 12m
W1
W2
Pwh
12m
heal
toe
U2
U1 U3
ton
h U
w
320 8 80 15.0
8 5.01
=× ×× =
× =
γ
100%=γ
wh
50%=0.5γ
wh
(
)
( )
ton
h U
w
160 8 80 15.05.0
8 5.05.02
=× ×× =
× =
γ
(
)
(
)
( )
ton
h U
w
1080 54 80 15.05.0
4 50 5.05.03
= × ×× =
+ × =
γ
Acting 58m from toe
Acting 59.33m from toe
Acting 36m from toe

m

ton
U U U P
u
1560 1080 160 320
3 2 1
= + + =
+ + =
Net uplift forces
SEEPAGE AND UPLIFT LOAD
93

94. •SECONDARY LOADS
•
Sediment load-nil
•
Hydrodynamic load-nil
•
Ice load-nil
•
Thermal loads-nil
•EXCEPTIONAL LOAD
•
Seismic load-nil
94

95. •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
•
i. Sliding factor, FSS;
•
ii. Shear friction factor, FSF;
•
iii. Limit equilibrium factor, FLE.
• 3. Overstress and material failure.
95

96. 1. Stability against Rotation and Overturning
moment g Overturnin
moment g Stabilizin
FOS=
Taking moment at toe of dam

α
m
m
m
2
3

80m
84m
1/3*80=26.67m
75m
50m 12m
W1
W2
Pwh
12m
heal
toe
U2
U1 U3

m

5.1 87.1
67. 26 36 3 33. 59 2 33. 59 1
33. 33 2 56 1
> =
× + × + × + ×
×
+
×
=
FOS
P U U U
W W
FOS
wh
It ranges from 1.5~2.5
96

97. 2. Stability against sliding of dam
59.0
2. 5359 / 3200
=
=
=
∑
∑
FOS
FOS
V
H
F
SS
It should not be permitted to
exceed 0.75 for normal load
combinations
i. Sliding factor, FSS;

α
m
m
m
2
3

80m
84m
1/3*80=26.67m
75m
50m 12m
W1
W2
Pwh
12m
heal
toe
U2
U1 U3

m

97

98. 2. Stability against sliding of dam
76.1
3200
2. 5359 8.0 62) 81.9 / 1000 3.0(
tan
=
× + ×
=
+
= =
∑
∑
∑
SF
SF
h
SF
F
F
H
V cA
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/m
2
(see slide 69)
A
h=T=B=62m

α
m
m
m
2
3

80m
84m
1/3*80=26.67m
75m
50m 12m
W1
W2
Pwh
12m
heal
toe
U2
U1 U3

m

98

99. 2. Stability against sliding of dam
1 76.1
>
=
LE
F
FLE=1.3 (seismic) ~ 2.0 (normal)
iii. Limit Equilibrium Factor, FLE:
For plane surface
FLE=FSF
99

100. •3. Overstress and material failure.
• The primary stresses determined in a comprehensive analysis by
the gravity method are as follows:
a)
vertical normal stresses, σ
z
, on horizontal planes;
b)
horizontal and vertical shear stresses, σ
zy
and σ
yz
;
c)
horizontal normal stress, τ
y
, on vertical planes;
d)
major and minor principal stresses, σ
1
and σ
3
(direction and
magnitude).
10 0

101.
α
m
m
m
2
3

80m
84m
1/3*80=26.67m
75m
50m 12m
W1
W2
Pwh
12m
heal
toe
Eccentricity and position of resultant
U2
U1 U3
100%=γ
wh
50%=0.5γ
wh

m

∑∑
= − =
V
M
x where x
B
e, ,
2
ton .
-. -
-U W W
V
2 5359
1560 2 2419 4500
2 1
forces vertical Total
=
=
+ =
=
∑
m ton
P
U U -U
W W
M
− =
×−
× − × − ×
× + × =
=
∑
4. 133183
67. 26
36 3 33. 59 2 58 1
33. 33 2 56 1
at toe moment Total
position of resultant
m x85. 24
2
.
5359
4. 133183
= =
B is the based width of dam=62m
101

102.
α
m
m
m
2
3

80m
84m
1/3*80=26.67m
75m
50m 12m
W1
W2
Pwh
12m
heal
toe
Eccentricity and position of resultant
U2
U1 U3
100%=γ
wh
50%=0.5γ
wh

m

∑∑
= − =
V
M
x where x
B
e, ,
2
m x85. 24
2
.
5359
4. 133183
= =
3B
m
B
33.10
3
=
3B
m
x
B
e
15
.
6
85. 24
2
62
2
=
− =− =
6B
6B
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

103. (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
m
ton
B
e
B
V
P
m ton
B
e
B
V
P
zu
zd
=






− =






− = =
=






+ =






+ = =
∑
∑
σ
σ
Normal shear stress at toe
Normal shear stress at heal
Allowable stress=25 kg/cm
2
=250 ton/m
2
Therefore, dam is safe against tension and compression
103

104. (b). Horizontal shear stresses
(
)
( )
0 0tan
tan
= − =
−
=
zu w
u zu w u
p
p
σ
φ
σ
τShear stress at upstream (heal)
Shear stress at downstream (toe)
(
)
( )
2
/ 93. 91 )3/2(89. 137
tan
m ton
d zd d
= =
=
φ
σ
τ
104

105. (c). Horizontal normal stresses
(
)
( )
2
2
2
/
28.
61
)3/2( 89.137
tan
m
ton
d zd yd
=
× =
=
φ σ σ
Shear stress at
downstream face (toe)
(
)
( )
2
2
2
/
80
0 tan 80
tan
m
ton
p
p p
w zu
u w zu w yu
=
− + =
− + =
σ
φ σ σ
Shear stress at
upstream face (heal)
105

106. (d). Principal stresses
For upstream face (heal)
For downstream face (toe)
with no tail water (p
w’=0)
(
)
( )
2
3
3
2
2 2
1
2 2
1
/ 80
/ 99. 34
0 tan 0 tan 199. 34
tan tan 1
m ton
p
m ton
p
p
u
w u
w u
u w u zu u
=
=
=
− + =
− + =
σ
σ
σ
φ φ σ σ
(
)
( )
0
'
/ 16. 199
)3/2( 189. 137
tan' tan 1
3
3
2
2
1
2 2
1
=
=
=
+ =
− + =
d
w d
d
d w d zd d
p
m ton
p
σ
σ
σ
φ φ σ σ
106

107. PROBLEM:
A concrete gravity dam has the following dimensions:
EMax water level = 305 m
EBed level of river = 225 m
ECrest level = 309 m
EU/S slope starts at 305 m
EU/S slope = (H:V)= 0.5:1
ED/S face slope starts at 300 m
ED/S Slope= (H:V)= 2:3
EC/L of drainage galleries at 8m d/s of u/s face
EUplift pressures:
at Heal = 100 %
at Toe = 0 %
at drainage gallery = 50 %
107

108. PROBLEM 2: EDensity of concrete = 2400 kg/m
3
ENo tail water
EConsider self weight, hydrostatic pressure and uplift pressure
Check the stability of damfor
•1. Rotation and overturning,
•2. Translation and sliding and
•3. Overstress and material failure.
108

109. PROBLEM 2:
CH
α
PTERH
PTTRH
 6:RPTORH
2
3
D6:6RNNORH
Wc
1
0.5
109

110. 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 uplif t may be taken as
equal to the hydrodynamic pressure at either end an d 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 th e reservoir is full
and there is no tail water when the reservoir is em pty.
Also calculate the various kinds of forces at the h eal and toe of the
dam.
Assume the unit weight of concrete=24kN/m
3
and unit weight of
water=10kN/m
3

111. PROBLEM 3
Date of submission: Nov 30, 2016

112. THANK YOU