Buoyancy on Precast Units

Not only should they be tied together, but they should be tied to the base. I would seriously consider adding more weight to the base as you are relying on the soil cover to prevent overall uplift...not very prudent!

I'm regretting to inform you of this fact. but whether you tie these hollow cubicles together or not, they are likely to float like a cork. Folks often empty concrete swimming pools for cleaning and painting only to find that the water table is higher than they think or they experience a major rain fall. They go to bed with an in ground pool only to wake up to find one that has popped right of the ground. Tanks that are placed in ground for petroleum storage are often pre-filled with sufficient water to prevent this from happening . Thus a tank that could contain 30,000 gallons of fuel never receives more than maybe 15,000 gallons. The petrol floats on top of the water. The suction pipes do not extend below the estimated water level. The measuring rods that are used to stick the tanks to check for the liquid level will turn a different color indicating the difference in the water level vs the petroleum level. This is how the folks in charge recognize that condensate water has risen to the level that some must be pumped out so that it does not find its way into your fuel tank.

TMF

Hello Toomuchfun,

They will not float like a cork if they are heavy enough to stay down. I did a preliminary calculation and found that the structure was heavy enough to prevent flotation if, and only if all parts are tied together and the soil is placed on top. The factor of safety against uplift is another issue. It is clearly not adequate, but the fact remains, as stated in the OP, the structure will not float.

If your concrete tanks are hollow why not fill them with flowable fill, a concrete material that flows like soup, and hardens fairly quickly. This would prevent the hollow areas from creating any possible flotation issues. If you need to bind the hollow containers together simply create matching holes in the top of the lower container and bottom of the upper container, off set the container joints and place a pre assembled rebar frame work in the openings. when the entire assembly is locked in place this way it will be much stronger and I doubt very seriously that it will float, unless the cavity in the center of all this assembly contains an air pocket sufficient to cause flotation. I have used flowable fill in a number of projects where I was working on state highway excavation and refill projects and the need to provide a stable subsurface was a necessity and there was insufficient time to compact suitable fill and prove the compaction with testing. The engineers consider flowable fill to be 100% compaction when it hardens, and that occurs fairly quickly.

As you have knowledge to work with these kinds of materials I believe that you are aware of the fact that we built ships out of concrete for troop transportation during the 2nd WW and that today we have barges that are constructed from concrete and that we construct floating docks and walk ways from hollow concrete building units. I watched a septic tank company really screw up a project when the pump truck emptied a tank that was located in an area where the water table was just below ground level. The now empty tank floated up about two feet out of the ground. Clearly the property owner was furious!

TMF

I am sure bael recognizes that it is an issue of displacement relative to weight, and while concrete (and steel) can not float , structure covered in a skin of concrete or steel could float if they have sufficient displacement to offset the weight of the concrete of steel. However, in this case the structure submerged is approximately neutral bouyant if fully strapped to the foundation (and the foundation was only a few inches thick). The foundation to support such a structure would be more than 3 or 4 inches thick, so it is likely that the structure will be negative bouyant and would not float, per se. However, recurrent rebound, infill and settlement could be an issue as the relative structural loads applied to the foundation soils vary substantially with variations in water levels. Also, if the sidewalls are not bedded in a non-expansive engineered fill, you could see the structure work its way towards the surface through shrink/swell effects in expansive materials, unless it has enough weight to sufficiently resist the swelling pressures.

Hello TMF,

Filling the void space with flowable fill does not leave you with much of a tank and, in any case, does not address the question in the OP. I am aware that ships have been built with concrete and if the walls are not too thick, they certainly do float.

Here is my calculation:

Base volume 12 x 12 x 2 = 288 CF

Tank volume 8 x 8 x 24 = 1536 CF

Lid volume 8 x 8 x 1 = 64 CF

Displaced volume 1888 CF

P/C volume 4 x 7.3333 x 24 x 8/12 = 469 CF

Dry weight of concrete = (288 +469 + 64)145 = 119,000#

Weight of displaced water = 1888 * 62.4 = -117,800#

Submerged weight of structure = 1,200#

Submerged weight of soil on top = 4,800#

Total submerged weight 6,000#

As the submerged weight is greater than zero, the structure will not float provided the parts are connected together, but the margin of safety against flotation is considered inadequate.

If the parts are not connected together, it will probably not float either because water will simply enter the void space and reduce buoyant force.

If they install sealant, like strips of tar sealant, between the precast sections (this is pretty common). These seals can retard infiltrations even when the sections separate a little (i have seen 1/16th gaps and the seal is sound). So he definitely must secure the structure to the base to stop this capacity to rise until the space increases enough to allow infiltration to offset bouyancy or add enough over burden. Any top subsection not secured could float until it separated from the remaining structure sufficiently to release air pressure and infiltrate water.

I agree. The pieces must be tied together and more gravity load is needed to provide a satisfactory design.

Oops, I forgot that the tank is buried in soil. We can use the submerged weight of the soil above the footing. It has an area of 144 - 64 = 80 SF and a depth of 27'. Assuming the soil to have a dry density of 100 pcf, the additional ballast is 80*27(100-62.4) = 81,000#.

It could even be argued that we could use a truncated pyramid with side angle of about 30 degrees to the vertical which would provide a greater safety factor against flotation.

On this basis, I believe that flotation is definitely prevented. But the tank walls have to be tied together and tied to the base with sufficient capacity to provide the desired safety factor.

Just a thought.

How are you proposing to seal the joints? Is there an issue about infiltration? You would have about 1500 psf of uplift pressure on the roof of the sealed tank (until the outside water could equilibrate by seeping into the tank). How do you keep the roof from floating off? The soil overburden submerged is only about 125 psf across the footprint. If you used a 8" thick reinforced concrete roof that would add only about 100 psf. If you tied the roof to the first section of precast walls, the 1st precast walls only add about 300 psf. Strap the entire walls and roof to the floor and you have a down pressure of 1200 psf for the walls, 125 psf for soil overburden, and 100 psf for an 8" roof for a total downward pressure of 1425 psf (less than bouyant uplift pressure). To minimize movement in the tank, i.e. from irregular settlement, soil expansion, soil rebound, etc., you want there to alway be a positive downward force on the foundation with minimal relative change in that force. Typically you would want a downward pressure of 2 to 5 times the uplift pressure. You would need another 100 kips of ballast to achive a SF of 2 against floating (about 43 cuyd of submerged concrete). So a pressure of 3000 to 7500 psf spread evenly across the foundation floor (this is not the footing load, that would depend on the footing design), depending on the amount of acceptable movement at the surface and the type of soils. It is highly likely that the structural foundation loads greatly exceed the allowable soil bearing pressure, typically recommended around 3000 psf to 4500 psf maximums (let alone the allowable settlements). It might be better to design a wider based structure that is shallower to the bottom and has more cover at the top. Some structures, such as some stormwater structures, can be allowed to have less weight as they allow infiltration and tend to rapidly equilibrate with changing groundwater levels outside the structure, plus the overlying facilities are easily repaired. Use, importance, and maintenance of the structure and any overlying facilities must be considered. Thus in some situations, you can also bed the foundation and walls in sand, and install weep holes (and flap valves) to relieve hydrostatic pressures outside of the walls, by allowing the structure to bleed in groundwater when pressure is sufficient (I realize this is a tank, and that is likely not a acceptable course of action).

Assume the joints are sealed tight becase they are or can be.

I do believe that increasing the base to that the required FOS against uplift (floatation ) is achieved. However, it would seem that the buoyant force acts in the vertical direction (upward) while the gravitational force of each component acts downward. In the general sense, if the gravitational forces (weights) are larger than the buoyant forces than the structure will not float and stability is assured?

If the buoyant force is larger than the grvaitational forces than the stucture will float. Hence the above-ground swimming pool nightmare.

Is it fair to assume that the buoyant force acts at the base only? Pushing the entire structure upward from the base? Each of the P/C units in and of themselves are not floatable so why wouldn't their self weight keep them in position above the base. If you attempt to separate each piece and draw a FBD, the forces acting on the base are the buoyant force pushing up and then you have the base itself and all the stacked P/C units pushing down. Looking at the P/C units I do not see how the buoyant force can push it up since the piece is not individually buoyant and there is also no horizontal surface for the buoyant force to act against.

Why does this logic not hold water - no pun indended here.

Hello guest,

You make an excellent point. How can buoyancy lift a thing which has only a vertical exterior surfaces? The individual precast elements cannot be lifted because they do not have a horizontal component upon which the pressure can act. You have convinced me that my previous reasoning was faulty.

I now believe that the entire structure will not float, even if the individual elements are not tied together.

Bouyant forces can act on the air in the tank and any bouyant liquids/gases transferring pressure to the top. If you took a plastic cup (filled just with air) turned it upside down and submerged it the bouyant force would act on the air in the cup and transfer pressure through the air to the sides and top of the cup. The pressure on the walls is in equalibrium with the water pressure outside, but the top is held down by weight of the structure and overburden (the weight of the structure increases per unit from the top down and full pressure is applied at the top). However, if the bottom was fully sealed, such that no water could enter, the bouyant force would fully act on the base of the structure. The base then transfers the load to the walls. If there is a leak in the seal the bouyant force acts on the air inside the structure and the base of the structure transferring the load to the top of the structure as air pressure or to the walls from the base. Thus worst case scenario is that the seal leaks at the base to such a degree that the bouyant force fully transfer the pressure to the air inside the tank and the air pressure transfers this increased pressure to the walls and the roof. Thus if the individual units are tied to the top, they will be lifted as the top sould be by air pressures developed from bouyant forces acting in the tank at the lowest point where air remains trapped and there is a leak in the tank (until the air pressure can be relieved through a leak higher up in the system).

Hello RCE,

I believe you are correct, and in any case, tying the precast elements together and also tying them to the base would seem to be a sensible and inexpensive precaution to prevent flotation. It would not have occurred to me to do otherwise, but in the spirit of the OP, I assume you would agree that, provided the void space in the precast elements is vented to the outside air, there is no theoretical requirement to tie the pieces together even if common sense suggests otherwise?

Yeah, venting would be a common design practice for most applications (some might use pressure release, rather than open atmospheric, though this is more common to steel designs). However, i have found it is not good practice to assume someone would vent the tank at atmospheric.

What does venting to the atm have to do with Buoyancy? What does the air inside the structure have to do with buoyancy? Archimedes would roll over in his grave!

Here's a suggestion. Consider a submerged cube. Compute the pressure force on each face of the cube. Then sum all vertical forces together. What you should get is the buoyant force, i.e. gamma times the displaced volume. This is the way buoyant force is derived in many textbooks (although often with an arbitrary shape, not a cube), and then they simply use gamma times V for the remaining problems.

The point of this is that the buoyant force is really created by the net effect of the vertical components of the pressure forces. If you properly account for all of the pressure forces on all of the faces of your structure, and are satisfied that your design accommodates them, you should be ok. However, if you cut the structure at any plane you can calculate the buoyant force at the plane and calculate the sum of the forces. Simple statics…

Venting permits water to rise up in the void, reducing the displaced volume of water.

Take a cup which floats in the water. Turn the cup over and it still floats (if it doesn't tip over). Now drill a hole in the bottom of the cup (which is actually at the top) and water rises into the cavity until the cup sinks. Archimedes...as you were!

Cup sinks only if the specific weight of the material, that the cup is made out of is greater than water. The fact that the structure contains water or does not contain water is irrelevant to the question. Be safe and assume empty.

The buoyancy calculation always assumes an empty structure as worse case since a full structure would be "best" case.

Oh, well. So much for practicality.

Obviously, if the material of the cup is lighter than water, it floats. I was thinking of a china cup...similar to concrete in specific gravity. If the walls are not too thick, it floats if unvented and sinks if vented.

The original post wanted to know whether the precast elements needed to be tied together to prevent flotation. The answer is yes unless the void space is vented, in which case the answer is no...hardly "irrelevant to the question".

Actually, the upside-down cup will only sink if the bouyant force is less than the gravitational force, as the cup will remain filled with air unless there is a vent. A cup will not allow water inside unless the air trapped inside the upside down cup can be released. The bouyant force applies as air pressure across the air/water interface just as if there was a solid bottom. If the cup were placed in rightside-up it would be subject to substantial bouyancy until the top was submerged, then it would fill with water and the specific weight of the cup material would determine if it would sink.

Now imagine the sections of the tank subjected to differential vertical settlement, shrink/swell, and skin friction. Could the base separate enough from the column to break a seal at the base and create the condition where we have an effect similar to that of the upside-down cup (as water can enter the tank at the base)? If this case could occur, then the bouyant force is applied to the top of the tank, and the top must translate that down through the column or separate from the column to vent the air pressure (unless of course there is a vent built in).

It does not matter if the tank is sealed or if the tank has 12 vents to the atm., the buoyancy is the same. Assume a empty structure and calculate volume displaced X gamma. The vent is irrelevant to buoyancy. Now take a section through the structure and analyze the structure at that plane (sum of forces in the vertical direction) Volume displaced at that plane X gamma = buoyancy and weight of the concrete structure above that point. Is it in equilibrium?

For the precast boxes, there are no buoyant forces if the joints are all sealed against the ingress of water. Water pressure acts normal to all surfaces. The stack of boxes has no horizontal surface upon which the pressure can act, so there is no buoyancy.

If a leak occurs in the joint between the lowest box and the base slab, then water enters, forms a horizontal surface with the trapped air and exerts a buoyant force on the combined area of the walls and the void.

If you vent the void, the air can escape and the buoyant force is simply water density (62.4 pounds per cubic foot) times the volume of concrete.

I agree! Good Answer