Buoyancy including weight of water? 1

[TehMightyEngineer]

Short question: I'm trying to figure out why you can't count the weight of water as resisting the buoyancy force on a buried concrete tank.

Long question: I've attached a picture of my understanding of how the buoyancy loads should work out. The various discussions I can find on here and elsewhere discuss using the buoyant weight of soil which is the soil density minus the density of water. This makes sense to me that the soil will effectively weigh less in water. However, shouldn't we then take into account the weight of water (effectively putting the 62.4 pcf back into the weight) as the water will weigh down the structure.

Essentially, I imagine that there is a block of water the width of the lip of the base slab and the height from the base slab up to the water table. This block exerts pressure in all directions; the vertical force holds up soil above it, the lateral force pushes on either the structure or other water, and the bottom force pushes the structure down (which combines with the weight of soil). Thus, this block is confined in static equilibrium.

Another way of looking at it is to imagine you take the structure and enclose it in a clear glass tank of no weight. To pick up the structure you have to take the soil, structure, and water with it. Now, obviously in real life if we pick it up the water will flow away and leave the soil behind but doesn't the confining action of the surrounding water allow us to take the weight of water into account?

The only example I can find in literature on this is the Portland Cement Association; Rectangular Concrete Tanks, Revised 5th Edition, example 1, page 5-10. This example starts out giving a weight of "moist soil" as 100 lb/cu.ft. and then in the buoyancy calculations uses a "conservatively light" soil weight of 70 PCF. However, it says nothing of taking this reduction to account for the presence of water unless that was already included in the "moist soil" weight; but I find it hard to believe they had a soil with an original density of 162.4 lb/cu.ft. (even 70+62.4 = 132.4 lb/cu.ft. seems high for anything but the most heavy of soils).

Maine EIT, Civil/Structural. Going to take the 1st part of the 16-hour SE test in April, wish me luck!

 

[PEinc]

You can't use the water on top of the tank to resist hydrostatic uplift. If you could, an inflated basketball could sink if submerged deeply enough. Air bubbles would not rise to the surface. The water on top of the tank has no shear strength. Therefore, the tank will push the water out of the way as the tank rises.

http://www.PeirceEngineering.com

 

[GeoPaveTraffic]

I see no reason that you could not count the water on the outside of the tank as resistive weight.

The more common method would be use the water level at the outside top of the tank, since any further increase in water level does not increase the net buoyancy.

Mike Lambert

 

[cvg]

water inside the tank can be counted, outside the tank cannot. water exerts a pressure in all directions at any point.

resolve the vector forces of the water pressure at any point and try to prove that there is not an equal and opposite force. for instance, put your hand in a bucket of water. hold it vertically and then horizontally. do you feel a lot more weight on your hand when you turn it horizontal? no, the pressure does not change.

 

[TehMightyEngineer]

@PEInc: Interesting analogy. I agree that the water on top really doesn't matter as the more water on top cancels out the more water on the bottom and we have no net change the deeper we submerge the structure.

@GeoPaveTraffic: I agree, no reason to have more water above the tank as it has no net change on the tanks buoyancy. So, you seem to disagree with everyone else? I suppose that at least validates my problem.

@cvg: Ah, that's a very good analogy. What I get from this is that, yes, the buoyancy of my hand doesn't change but the resistance to removing my hand does (it's much easier to remove my hand if I point it down then if I cup it and take a bunch of water with me). Hmmm, that does get me thinking, though. I guess what would happen is this extra water would only SLOW the structure from rising (as it rises farther it sheds water and rises faster). Hmmmmm, I think finally get it, can you confirm I'm on the right track?

I suppose a good analogy/question would be, if I put a basketball underwater and put a upside down parachute on it, will the basketball rise? I would say, "yes" but it would do so very slowly. Essentially what my original problem was thinking that if someone had a big enough parachute and jumped out of a plane they would hold still. Obviously this isn't the case.

Maine EIT, Civil/Structural. Going to take the 1st part of the 16-hour SE test in April, wish me luck!

 

[cvg]

yes, you are on the right track and the effect you describe is the shear resistance of your hand moving through the water or the parachute moving through the air.

 

[TehMightyEngineer]

@Cvg: Excellent, that's a big help, star for you (though it means that I may have screwed up a structure for buoyancy, meh). I blame the PCA's tank example, that was terribly misleading.

Maine EIT, Civil/Structural. Going to take the 1st part of the 16-hour SE test in April, wish me luck!

 

[Kuhuh]

I don't think you would want to count the water in the tank. While it does count towards the force keeping it sunk. You should always design for operator error, if they were to drain the tank for cleaning/ maintenance that bad boy will shoot out the ground just like Bullwinkle.

 

[TehMightyEngineer]

@Kuhuh: Well, here's where I stand.

We designed a 35 foot deep wet well that takes combined sewage and storm-water and pumps it into a collection system. It was designed, fabricated, installed, and is buried on-site ready for use. However, the engineering firm who designed the system (Who was hired by the engineer who was hired to do the job, it's a wonderful mess. We don't even work for them, we work for the pre-caster.) is making a stink about reviewing everything (2 years after the fact) and caught this error in our buoyancy calculations. Our fault but we're trying to make it work "as is" if we can. If I assume an extreme case and a service level case I can get it to work (barely).

Extreme case involves no conservative weights of concrete or soil and I assume the tank is empty. This results in exactly a 1.0 safety factor. This seems okay to me as this is a wet well it would be quite unlikely that they would have the tank empty at the exact same time we get a 50 year storm and as I don't assume any shear angle to the resisting soil I figure it's conservative.

The service level case is where I assume the tank has a minimum of 8 feet of water but does not include the pumps and conservatively uses weights for the concrete and soil. This results in a safety factor of 1.10.

I of course have to run it by my P.E. and then see if the reviewer likes this. In the end if they need to modify it they don't have to do much to get it to the required weight. They can just excavate the top barrel section and pour a cast-in-place ring of concrete around it with doweled in epoxy rebar.

P.S. While I was writing this my P.E. got back to me. We're going to do similar to above but calculate and take into account the soil "cone" rather than assume a 90 degree shear plane. That should be good enough for everyone. Lesson learned and nobody burned during it.

Maine EIT, Civil/Structural. Going to take the 1st part of the 16-hour SE test in April, wish me luck!

 

[TehMightyEngineer]

Hmmmm, now my boss has me going back around.

So, obviously IF you get it moving up it will just push water out of the way. However, what if it doesn't move up and is static. Don't you have to break the force of the water to get it moving? Or is this simply the case but it's not really possible to calculate this resistance? It just seems that pushing the water out of the way has to offer some resistance.

Or maybe it doesn't since fluids are weird.

I guess I need something I can give to my boss that shows conclusively how this is supposed to be done because otherwise he wants be to take it into account. The PCA example I quoted is very unhelpful and I can't find any others.

Maine EIT, Civil/Structural. Going to take the 1st part of the 16-hour SE test in April, wish me luck!

 

[Kuhuh]

first I think you should just toss this entire idea of the water forces above the wetwell as I don't really see much justification for its theory. However, it seems there is much debate as most design cases entail. It really comes down to how comfortable you feel. While most response I have received say a SF=1 is good enough others say if you don't use the skin friction of the soil or use only the weight of soil within the vertical plane from edge of footing up you do not need a SF. here is an example of a surface exposed manhole. Hope it helps.

http://www.concrete-pipe.org/pdfdd/DD_41.pdf

 

[TehMightyEngineer]

@Kuhuh: Thanks for the example, that's a huge help.

Maine EIT, Civil/Structural. Going to take the 1st part of the 16-hour SE test in April, wish me luck!

 

[aeoliantexan]

Most of us worried through this puzzle at one time. I like to draw a free-body diagram; they don't lie. The forces downward include the structure, its contents,and the soil and water above the footing extension beyond the structure. Upward forces include the pressure of the water against the bottom of the structure and footing extension times the area against which it acts, plus the reaction of the soil grains against the footing and extension. (Remember that both the water pressure and the effective soil stress act against the full area of the foundation, because the soil grains touch only a tiny area.) If the soil reaction is zero, the structure is trying to float. Never mind that the water has to flow around the edge of the footing; slow flotation is as destructive as fast. There will be some shear resistance of the soil along the vertical-sided surface you drew to calculate the soil and water weight, so the soil will actually shear at an angle, the "cone" your boss mentioned, and the tank will have to pick up the buoyant weight of the soil between the vertical plane and the angled plane. After you add that in, the downward forces should be at least equal to the upward water force times the factor of safety you have chosen to use (or some code dictates).

Here is one more thing to worry about: before all that soil weight is mobilized to resist flotation, the loose soil that the contractor dumped on top of the footing must be compressed by the upwards movement of the footing. That compression might be a few inches. Can your structure stand that movement? If not, compaction of all the backfill becomes very important, but it is very hard to enforce. I prefer to get a factor of safety of 1.0 without counting the backfill, then add in the backfill to get an acceptable factor of safety.

 

[paddingtongreen]

If you are taking the upward water pressure at the bottom for the full depth of water, you must take the downward pressure on top. If you are simply calculating based on the weight and volume of the tank and the density of water then the pressures disappear.

Because the pressures are real, more compression on the tank, I prefer to use the pressures.



Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[PEinc]

Buoyant force equals the weight of the displaced water, no matter the depth of water over the top of the structure.

Assume a 10' tall void with 10' of water above. Downward water load on top is 10 x 62.4 = 624. Upward pressure on bottom of void at 20' deep is 20 x 62.4 = 1248. Net = 1248 - 624 = 624 up.
Assume a 10' tall void with 20' of water above. Downward water load on top is 20 x 62.4 = 1248. Upward pressure on bottom of void at 30' deep is 30 x 62.4 = 1872. Net = 1872 - 1248 = 624 up.
Assume a 10' tall void with 300' of water above. Downward water load on top is 300 x 62.4 = 18720. Upward pressure on bottom of void at 310' deep is 310 x 62.4 = 19344. Net = 19344 - 18720 = 624 up.
Water on top of the structure, and below the normal water level, does not reduce uplift. As long as the water above the structure is "connected" to, is level with, and is part of the water level around and below the structure, the water above will not reduce uplift.

http://www.PeirceEngineering.com

 

[TehMightyEngineer]

[head spinning in circles]

Okay, this is the only thing that I can seem to find that makes everything agree.

There are TWO methods to tackle this problem.

Method One: Archimedes. You calculate an uplift force based on the VOLUME of water displaced. This requires that one ignore water above the structure and thus you must reduce soil by the density of water. The resisting force is the weight of the structure and any soil it takes with it. Simple (though this ignores force transfer through a structure but, unless you're building at the bottom of the ocean, I doubt this would ever control a design.

Method Two: Pressures. You construct a free-body diagram where water pressures act normal to the plane of the structure. Water pressure is effectively a function of depth and, given a typical rectangular box structure, the pressure on the bottom is uniform and equal to the density of water times the depth. However, if we have an overhang on the structure, or some surface where the normal direction has a vertical, downward component, THEN we take the water pressure DOWNWARD on that surface. This pressure would counteract the buoyancy force. This works out to the same as method one because the little strip of downward water pressure is balanced out by a slightly higher uplift load than method one. So, for this case it's more complex but, technically, more accurate.

Please someone tell me I have it right. It seems to me that all this confusion stems from the fact that you can either consider the water above or not it's just that you have to be consistent with the design methodologies.

Maine EIT, Civil/Structural. Going to take the 1st part of the 16-hour SE test in April, wish me luck!

 

[paddingtongreen]

You have it right. Your Method One does not give you design pressures for the walls, top and bottom of the tank, Method Two does.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[TehMightyEngineer]

Oh thank goodness.

Maine EIT, Civil/Structural. Going to take the 1st part of the 16-hour SE test in April, wish me luck!

 

[PEinc]

paddingtongreen is correct. Method Two gives pressures at different locations on the structure, These pressures are used to design the slabs and walls. However, I believe that the original question was about buoyancy only. Method One is used to see if the structure will float up. Therefore, my previous answer addresses buoyancy.

http://www.PeirceEngineering.com

 

[chicopee]

Looking at the diagram, I would think that the soil is fully saturated and that saturated soil would be the weight on the top of the tank.