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!

 

[Archie264]

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?

 

[SlideRuleEra]

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.

http://www.SlideRuleEra.net

http://www.VacuumTubeEra.net

 

[Archie264]

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

 

[MiguelPenaWSE]

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

 

[DamsInc]

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.

 

[DamsInc]

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

 

[jayrod12]

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.

 

[MiguelPenaWSE]

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!

 

[cvg]

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

correct, see attached figure from design of small dams which shows exactly that.

 

[jayrod12]

See the pdf I attached. Granted this doesn't account for the fact that the water is flowing. My point is the 1m of water above the dam still causes vertical stress on the water at the top of the dam level.

The 0.5*(1+6)*5 is for the area of the trapezoid.

 

[SlideRuleEra]

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:

http://www.SlideRuleEra.net

http://www.VacuumTubeEra.net

 

[MiguelPenaWSE]

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?

 

[SlideRuleEra]

MiguelPenaWSE - The excellent book that cvg quoted, "Design of Small Dams" is available as a free download from the US Bureau of Reclamation. There is another book, "Design of Gravity Dams". You may want to get both. Here is the link, look at the top of the page:

http://www.usbr.gov/pmts/hydraulics_lab/pubs/manuals_monographs.html

http://www.SlideRuleEra.net

http://www.VacuumTubeEra.net

 

[cvg]

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

 

[MiguelPenaWSE]

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.

 

[IDS]

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/

 

[DamsInc]

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.

 

[MotorCity]

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.

 

[jayrod12]

MotorCity,

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