Arch Dam

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DESIGN OF ARCH DAM
Presented by- AVIJIT DAS 14PCE066 M. TECH, 2ND
SEM WATER RESOURCES ENGG.
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CONTANTS

• Definition
• Types of arch dams
• Constant Radius arch dams
• Variable radius arch dams
• Constant angle arch dams
• Forces acting arch dams
• Design theories of Arch dams
• Thin cylinder theory
• Limitations of thin cylinder theory
• Theory of elastic arches
• Conclusion

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What is Arch Dam ?
It may be defined as a solid wall, curved in
plan, standing across the entire width of the
river valley in a single span. Its body is
usually made of cement concrete, although in the
past Rubble and stone masonry are also used. It
will structurally behave Partly as a cantilever
retaining wall standing up from its base, and
partly the load will transfer to the two ends by
horizontal arch action.
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Monticello Dam in California
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Types of Arch Dams

• Three Types of arch dams-
• Constant Radius Arch Dam
• Variable Radius arch dams
• Constant angle arch dams

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Constant Radius Arch Dam
Constant radius arch dams are that in which, the
radii of the outside curved surface are equal at
all elevation. The centers of all such circular
arch called Extrodos, will therefore evenly lie
on the vertical line. However, the Introdos has
gradually decreasing radius from top to the
bottom.
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Constant Radius Arch Dam
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Variable Radius Arch Dam
These are the one in which the radii of the
Extrodos curves and the Introdos curve vary at
various elevation. Maximum at the top and a
certain minimum at its bottom. In a typical
design of dam the d/s face of the dam at the
central line is vertical while at all other
location there is a better on both side except
at the abutments.

• Advantages of Variable Radius Arch Dams
• Greater Arch Efficiency.
• Useful to meet foundation requirement
• Save of concrete.

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Variable Radius Arch Dam
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Constant Angle Arch Dam
It is a special type of variable radius arch dam,
in which the central angles of the horizontal
arch rings are of the same magnitude at all
elevation. However, it is economical, saving
30-40 concrete in compare to constant radius
arch dam.
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Forces acting on Arch Dam

1. Water Pressure
2. Uplift pressure
3. Seismic forces
4. Silt pressure
5. Wave pressure
6. Ice pressure

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Arch stress analysis
Elastic ring Theory
It is based on the application of classical ring
theory for simple single curvature arch dam of
modest height. This method is appropriate for
preliminary analysis of constant radius
profile. This theory consider the water load
only. Self weight stresses being determined
separately and super imposed if significant to
the analysis. In this method uplift force is
normally neglected. For analysis the dam is
subdivided into discrete horizontal arch elements
of unique height. Vertical cantilever action is
thus neglected.
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Thick Ring Stress analysis
The discrete horizontal arch elements are each
assumes to form part of a complete ring
subjected to uniform external radial pressure Pw
from the water load. The compressive horizontal
ring stress, ?h for radius R is,
Where, Ru and Rd are upstream and downstream face
radii respectively of arch element
considered For R Rd , Pw ?wZ1 ,
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Thin ring stress analysis
If the mean radius Rm is very large in comparison
to Tr it may be assumed that Rm Ru Rd And
consequently the stress ?h through the ring
element is uniform. The classical thin ring
expression is
The maximum tangential stresses will therefore be
those generated at the abutment
Factor Kr is a function of 2?
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Thin Cylinder Theory
In this theory the arch is treated as a thin
cylinder shape resting freely on the abutments.
The whole water pressure is supposed to be
transferred to the abutments. The weight of the
arch is not taken withstand the water pressure
and the same acts normally on the surface of the
dam. In practice however a arch dam is never a
cylindrical completely and therefore the
stresses computed are approximate. The stress
distribution at a cross section of arch is taken
to be uniform. This method is useful for
preliminary design of surge dam.
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Limitations of thin cylinder theory

• The arch sections are not thin cylinders.
• Arch sections are not free at the abutment as
  it assume.
• The shearing as well as bending stresses in the
  arch are not
• taken into account in this theory.
• The analysis is based only on the water
  pressure.
• Stress due to reach shortening is also not
  taken into account.
• The shrinkage in concrete is also not
  considered.
• Yielding of abutments and stresses are not
  accounted in this theory.

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Theory of Elastic Arches

• In this theory the arches are subjected to
  additional forces, such as
• Temperature stresses due to temperature
  changes.
• Shrinkage stresses due to setting of concrete.
• Stresses due to yielding of abutments.
• Stresses due to rib shortening.

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Conclusion
Since the design and construction of an arch dam
is very complicate, requiring extraordinary
skill for erecting shuttering in the field, it is
generally preferred in practical life to
construct gravity dams. And that is why we found
only one arch dam in our country that is the
Idduki Dam, across Periyar River in Kerala
state, as against several hundreds of gravity
dams. This arch dam too is not a simple arch dam,
but a shell arch dam.
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Idduki Dam, across Periyar River in Kerala state
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