Hydrostatic pressure on Concrete Dam 4

[MiguelPenaWSE]

Concrete Dam Stability.
I have a question regarding hydrostatic pressure.

Please see picture.

For purposes of the design, we will design in 1 meter intervals.
Let's assume that the toe of dam is set at 100 meters while the top of the dam (weir) is set at 105 meters.
Under sunny day conditions, water level is right at 105 meters (no water flowing).
Under flood conditions - 100 yr design storm -, the water level is at 106 meters. (1 meter higher than the top of the dam). Lots of water flowing over.

when calculating the hydrostatic pressure under sunny day conditions, h (height of head water) is 105m-100m = 5 meters.
Therefore - hydrostatic pressure is = (1/2) * (unit weight of water = 9810 N/m3) * (1m section) * (h = 5m)^2
Sunny Day - Hydrostatic pressure = 122,625 Newtons

Now, when calculating hydrostatic pressure for flood conditions... Should h be 6m? or should it be 5m?
Is the 1m of water height over-flowing taken into consideration>?

This is where I am getting confused.

Thanks!

 

[racookpe1978]

Now wait a minute. Weight a minute? 8<)

Look at 5 meter - exactly full case. No water movement.
That weight of water pushes down behind the dam, and the water at the extreme bottom of the dam (pushing horizontally between the dam and the dirt/dock/soil below the dam to undercut the dam and to push it downstream) reflects 5 meters of depth. Water at the dam base is static - as noted above.

Now - dynamic situation at the top - water is flowing over the top of the dam, may (or may not) be actually touching the dam/spillway face (most spillways I've seen try to guess flow rates and thus water water speed and minimize surface scarring, erosion and pressure). Then it hits the bottom and splashes turbulently in all directions. Surely, these irregular and turbulent banging and splashing and impact waves on the base and concrete and bottom of the dam can't be "relied on" as a known "horizontal design force" like a wier or stagnant force behind the dam!

However, go back to the top of the spillway: The water going over has a velocity sidewyas, but it also still has a weight "down" that is significant. That moving water's weight "down" forces down on the still water just behind the dam top at 5 meters. The weight of the total water at 4 meters = the first 1 meter depth (1 meter moving water + 1 meter stagnant water). The weight of water at 3 meter elevation = 1 meter moving water + 2 meters moving water, etc.

Further, the weight of water behind the dam far upstream of the spillway does push stagnantly down and sideways. The force at the bottom is due to 6 meters of water conservatively - IF your prediction of only 1 meter of water flowing across the spillway is correct.

 

[jayrod12]

Weight a minute?

Bravo.

Your rationale is exactly what my sketch shows. I've assumed no contribution on the downstream side of the dam. and a full 6m of water on the upstream side. The pressure distribution is based on 6m depth, the actual lateral force is only 5m of dam height accounting for the 6m of water via trapezoidal distribution.

 

[rb1957]

this is just so much water over the dam ...

another day in paradise, or is paradise one day closer ?

 

[msquared48]

You're all wet rb.

Mike McCann, PE, SE (WA)