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Hydrostatic pressure on Concrete Dam
4

Hydrostatic pressure on Concrete Dam

Hydrostatic pressure on Concrete Dam

(OP)
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!

RE: Hydrostatic pressure on Concrete Dam

It's bound to be 6m, right? Surely that extra meter of water doesn't somehow weigh less just because there isn't concrete on one side of it.

Or, conduct a thought experiment: say you're an Egyptian on a chariot chasing Israelites through an unexpectedly dry Red Sea bed and the walls of water on each side of you suddenly gave way. The water might crush you before it drowns you, right?

RE: Hydrostatic pressure on Concrete Dam

5 meters. Water pressure has to act perpendicular to a surface. Above 5 meters, there is no surface on the upstream side off the dam. There will be other forces, such as the weigh to the water above the dam and forces from flowing water, but not the one properly called "hydrostatic pressure". Just remember that for hydrostatic pressure to be applicable, the water has to be potentially exactly that... static. Water deeper than 5 meters cannot be static.

www.SlideRuleEra.net idea
www.VacuumTubeEra.net r2d2

RE: Hydrostatic pressure on Concrete Dam

Ok, well, glad I don't design dams then.

RE: Hydrostatic pressure on Concrete Dam

(OP)
SlideRuleEra
Thank you so much!
Your explanation made complete sense.

RE: Hydrostatic pressure on Concrete Dam

The question isn't whether H is 5m or 6m, because either value will result in the wrong answer. The pressure above the top of the dam is 0. F=t(1/2)(gamma)(6)^2 - t(1/2)(gamma)(1)^2. You need to look at the actual pressure distribution and understand where that formula comes from. You will then need to derive the location of the force because that will no longer act at the 1/3 point, so you need to account for that too.

RE: Hydrostatic pressure on Concrete Dam

That is just for the upstream force by the way. The weight of the water above the section needs to be accounted for seperately.

RE: Hydrostatic pressure on Concrete Dam

4
I disagree with sliderule in this case (it doesn't happen often)

The 1m of water above the face of the dam changes your pressure distribution from a triangle to a trapezoid.

Now your pressure at the top of the wier is equal to gamma, at the bottom of the wier it is equal to 6*gamma.

Force = 0.5*(1+6)*gamma*5 = 171.7kN (40% increase) acting at 1.905m from the toe. Therefore your overturning moment is 327 kNm which is an approximate 60% increase in overturning moment.

RE: Hydrostatic pressure on Concrete Dam

(OP)
Jayrod12

Could you please explain your input...And thank you!

Water creates a pressure that forms a right triangle with two equal sides... Therefore h is square (h^2) when calculating hydrostatic pressure.

Since there is water overflowing the weir, the above rule does no longer apply. However, I can not visualize it in my mind.
Could you please draw a pressure distribution figure?

Or maybe explain where why you are using (1+6) in your equation.

Thanks!

RE: Hydrostatic pressure on Concrete Dam

jayrod12 - You are right. The hydrostatic force does have to act perpendicular to a surface, but that does not rule out the surface can be completely below water. IMHO, the overturning moment will be more complicated because of the water's weight and dynamic forces.

MiguelPenaWSE - I have marked up you original sketch to show what jayrod12 pointed out:

www.SlideRuleEra.net idea
www.VacuumTubeEra.net r2d2

RE: Hydrostatic pressure on Concrete Dam

(OP)
CVG
Thanks for including this picture!

To continue with this topic...
I have a question regarding Friction Force (FF).

FF = Sum of Vertical Forces * Friction Coef.

Friction Coef (Concrete on Concrete OR Concrete on Bed Rock) = 0.4 ~ 0.5

For the vertical forces...
Downward force from the weight of the concrete (13140 N)
Downward force from the weight of the water above the structure (456 N)
Upward force from uplift (3794 N)

FF = (-13140-456+3794)*(0.4)
FF= (-9802)*(0.4)
FF= -3920 N

This friction force is applied against HeadWater Hydrostatic Pressure...

Any thoughts on such approach?

RE: Hydrostatic pressure on Concrete Dam

forces are fine, but you might ignore the downward force of water, it is relatively small. you may also include tailwater on the downstream side of the dam which exerts a lateral force in the opposite direction.

Your friction coefficient might be low. suggest the following as a reference from the army corps

RE: Hydrostatic pressure on Concrete Dam

(OP)
SlideRuleEra, CVG, Jayrod12 & damsInc...

I would like to thank you guys for your help.

I now have a better understanding of the different approaches to take.
I will download both books and utilize them when needed.

My boss came in and agreed with what I had computed (following yall's input).

Have a great evening everyone.

RE: Hydrostatic pressure on Concrete Dam

Quote:

forces are fine,

I don't think so. For the weight of the dam you need the full weight of a 1 metre slice. Your sketch doesn't give dimensions, but clearly it will be much more than 13.1 kN. For the upward force of the water you need the pressure distribution over the full width of the base. I don't know how that is defined but presumably the suggested texts will give some guidance. This, along with the overturning forces due to water flowing over the top of the dam, are the main areas where some experience in design of dams is necessary. I'm not a dam engineer, but I'd suggest a full review of your work by someone who is.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Hydrostatic pressure on Concrete Dam

I wanted to add that the "Design of Small Dams" document SlideRuleEra posted is a great resource. Another good one is USACE "Gravity Dam Design" which is free online. Not sure of your location, but in Canada we also have the CDA Dam Safety Guidlines (not free). There is a free program called CADAM, developed at Ecole Polytechnique de Montreal. The user manual for the program is a great summary of the various methods of analysis. The link seems to be broken on the website but I've attached the manual here.

For the friction, current practice is to use the Mohr-Coulomb approach using a friction angle and value for cohesion.

Your questions are fairly basic (I don't mean that to sound condescending), so obtaining the above resources and reading through them is your best bet to learn. They can explain the basics better than this web forum can.

RE: Hydrostatic pressure on Concrete Dam

Maybe I am missing something, but if water flows over the dam then you have equal and opposite pressure on both sides of the dam resulting in no net pressure on the dam. Seems like a mute point if we are talking about hydrostatic forces only.

At that point you would have bigger problems.....depending whats on the other side of the dam.

RE: Hydrostatic pressure on Concrete Dam

MotorCity,

I was thinking more of a spillway where you wouldn't count for any water on the backside.

RE: Hydrostatic pressure on Concrete Dam

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.

RE: Hydrostatic pressure on Concrete Dam

Quote (racookpe1978)

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.

RE: Hydrostatic pressure on Concrete Dam

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

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

RE: Hydrostatic pressure on Concrete Dam

You're all wet rb.

Mike McCann, PE, SE (WA)


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