Dams are some of the most marvelous structures mankind has ever built.
But how do they hold back entire lakes?
In this video, we dive deeper into the hydrostatic forces exerted on a dam, and the mechanism
by which the dams withstand these forces.
To understand how a dam works, we need to understand what hydrostatic forces are.
Hydrostatic forces are loads that fluids at rest exert on their containers, which in this
case is the dam and the surrounding terrain.
One easy way to understand the origin of the hydrostatic forces is to investigate the interactions
within the body of water.
Let s model the water in a dam as tiny blocks of water.
Due to gravity, the weight of the upper block presses down on the lower block which tries
to relieve the pressure by displacing away.
If there is no side support, then the water will spread out until an equilibrium is reached.However,
in our case one side is supported by the dam.
This means that the dam needs to absorb the pressure.
This side pressure depends on how hard the water is being squeezed.
If we add more water on top, then the additional weight presses harder on the bottom block
which increases the side pressure.
This is well illustrated with a barrel with holes along its height.
The water stream coming off of the lower holes will reach farther away.
Since dams can be extremely tall, the hydrostatic pressure at the base of the dam can also be
extremely large.
This triangular pressure diagram is the main force that the dam needs to resist.
Gravity loads are the main consideration for dams, so that's what we'll focus on here but,
keep in mind that there are also load considerations such as earthquakes.
If you want to get an idea how earthquake loads act check out our video on that.
Now that we have an understanding of the main load which dams feel, we can start thinking
of a suitable structure to resist it.
Let's start with the most basic structure, a concrete block, and iterate to something
more efficient.
Obviously, this structure is not very efficient.
We have equal amount of material along the entire height but unequal load distribution.
Tapering the structure would be a more efficient use of the material, this way the higher loads
are met with more material and vice versa for the lower loads near the tip of the dam.
We can go a step further and curve the structure, this way we can eliminate or at least reduce
tension loads and engage more of the dam in compression with arching behaviour.
From one of our previous videos, we saw that concrete is superior in resisting compression
forces when built into arches.
Already, we have an extremely efficient structure that starts to look a lot like some iconic
dams from the real world.
One problem with arches is that they produce large thrust forces that the dam will need
to resist and therefore the surrounding valley as well.
Thrust forces are horizontal forces that keep arches compressed.
These forces originate at the centre of an arch and keep each half in compression, before
being resisted at either end of the arch.
Therefore, a requirement for an arch dam is a solid rock foundation that can absorb the
large thrust forces.
Clearly not all dams take an arch shape.
If the arch is the most efficient shape, why do we have dams like the Three-Gorges Dam that
maintains a straight line across its valley?
The explanation to this lies in shape of the valley.
Narrower valleys are more suitable for arch dams.
The valley of the Three-gorges dam is 2.3 km long, if this structure took the shape of an arch
with the same height to width ratio as the Hoover Dam then the structure would have been
almost 500m longer than what it is now.
Instead of making a longer curved structure, the 3-Gorges Dam takes a more massive straight
shape.
Straight dams also have their own advantages.
They are easier to construct and do not necessarily need solid rock foundations as arches do because
they use a different mechanism to transfer the hydrostatic loads.
These dams are also known as gravity dams because they use their massive weight to produce
large enough friction forces to hold back the water reservoir.
Due to their massive size, these structures usually do not suffer from high internal stresses.
The governing failure mode comes down to the sliding resistance between the dam and the
ground beneath it.
Often gravity dams incorporate a shear-key which helps generate a larger resistance to
sliding.
As an example, we made a low detail model of the Three-Gorges Dam and analyzed it under
hydrostatic forces.
As seen on the model, the maximum stress in the monolith is way below the yield stress
of concrete.
Keep in mind this model is way oversimplified and an actual design is much more rigorous
and takes hundreds of man hours design against all possible failure modes.
Failure modes can be intuitive like the entire dam overtopping or sliding at the base, or
the concrete failing structurally.
But there are also some less intuitive failure modes which are very relevant such as seepage
and seismic failures.
One example of these concerns is the Mullaperiyar dam in India.
There is a very high chance that I miss-pronounce the name so please forgive us for that.
The dam was built more than 125 years ago,
and construction materials and engineering practices have changed a lot since then.
As you can see in this cross section, the
dam was constructed using uncoarsed rubble masonry in essence randomly sized and randomly
placed stone and surkhi mortar-which is basically brick powder, lime and water.
During the 1980s, concrete was also added to the downstream side to strengthen the old
structure, but the upstream water could not be drained to perform a full restoration.
Today, the dam is experiencing seepages issues where water under high pressure seeps through
small cracks in the structure and carries out the surkhi mortar with it.
Over time, this removes material (and thus strength) from the core of the dam which can
lead to failure.
Additionally, the dam is know to be in an earthquake prone area without being designed
as such.
To learn more about how earthquake damage occurs, check out one of our other videos.
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