# Settling of unevenly loaded storage tank

Suppose I have a concrete tank, round, vertical, diameter in the range 16m-24m. One half the floor is filled with gravel or concrete to a height of maybe 2 meters. When the tank is empty, that will mean I have about 5 tons per m² more weight on this half, when the tank is full (with water or a slurry that's mostly water) it's still 3 tons (assuming 2.5 t/m³ density which is exact enough for my ballpark). Most of the times (>90%) it will be full. The tank will be above ground, 8-10 m high.

I want to know if the tank will tilt during its lifetime, say 20 years. I'm not a civil engineer and I have no feeling for the numbers involved. My gut feeling is that my tank will tilt visibly in a matter of a few years and that my idea is not feasible as is. Can someone weigh in and comment on ...

• Will I have tilt/uneven settling problems? At what magnitude over the tanks lifetime?
• What's the easiest (=cheapest) remedy, leaving the tank interior alone?

Clarifying points: The tank is not yet built or even planned. It's just an idea I'm thinking about that calls for half filling the tank to create a sort of funnel. I wonder if this idea is worth pursuing, and uneven loading/settling is one issue want to consider. I'm not in the "call a structural engineer and let him calculate the static" phase, I'm in the tossing around harebrained ideas in my skull phase. I'm sure such a tank can be built to last for 20 or 200 years, but at what price?

• What is the total weight of the tank, as compared to the weight of the asymmetric fill? My gut feeling is that the latter is insignificant with respect to the former. The real question is how does the pressure on the ground vary across the base of the tank, and then designing the foundation, etc. to take this into account. – Dave Tweed Jan 29 '15 at 13:21
• total weight is the content (hieght -1m water column) plus the concrete, say 25 cm for groundplate and wall and possibly a bit more (with screed and so on) for the ceiling. The major part will be the content, then you have (say) 9 water column vs 7 m wc + 5t/m² => 9t/m² vs 12t/m² – mart Jan 29 '15 at 13:57
• What kind of soil is the tank going to sit on? Has there been a geotech report? – Ethan48 Jan 29 '15 at 15:21
• I believe @Ethan48 is on the right track that it most likely will be more reliant upon the foundation than the asymetric loading of the tank itself. If the tank foundation is designed (with correct design margin) to support the greatest total weight of the tank there may not be any issue regarding asymetrical loading. – Dopeybob435 Jan 29 '15 at 15:24
• Assuming you are referring to a Vertical round and not Horizontal round, correct? Was the tank originally designed to hold aggregate rather than a liquid or is this an aftermarket jerry rigging? If it was not originally designed for asymetrical storage or aggregate storage it would be a good idea to bring in a Structural Engineer to verify the design is able to within the stresses without failure. Things such as skin loading of the walls and off centerline center of gravity could cause the tank to rupture prematurely or even topple (not related to settlement) – Dopeybob435 Jan 29 '15 at 15:33

Here's a really (and I mean really!) quick and dirty set of calculations that might give you an idea of the magnitudes of settlement you could be dealing with.

The settlement potential of the tank location can be determined a number of ways, but probably the best thing to do would be a plate load bearing test. The test can be run to simulate the range (though not the duration) of loads you are expecting. A test like this will give you a spring constant $k$ that represents the "modulus of subgrade reaction" of the bearing soil (for the tested loading range). However, it's a short term test that doesn't take into account creep, so the long-term $k$ value will be lower.

In general, a short-term $k$ will run from something like 80pci for a very soft clay to something like 250pci for a very dense sand (caveat: this is just from the top of my head without looking anything up).

So let's use the worst case scenario here, and to take into account creep, let's do what geotech engineers do best and slap a 2.5 safety factor on it. So we have about a 30pci modulus of subgrade reaction.

Let's also assume that most of the differential settlement will occur as a result of the uneven loading of the empty tank, and that the emptying/filling of the tank is going to have a negligible contribution to the differential settlement. This isn't too terrible of an assumption, since the difference in applied surface pressure (which determines differential settlement) is much greater in the empty state, and it's also conservative because it will only be empty 10% of the time anyway.

So here we go (I'm American, so we're doing everything other than what you gave for dimensions in imperial-scum units first and then converting - sorry!):

$k = 30 \frac{lbf}{in^3}$, $\gamma_{concrete}=150\frac{lbf}{ft^3}$, $H_{concrete}=2m$

Applied pressure under half the tank: $q_c=H_c\times\gamma_c=0.98ksf=5.3 \frac{tonf}{m^2}$

Settlement under loaded half of tank: $S=\frac{q_c}{k} = 0.23in = 5.8mm$

If we assume the other side of the tank does not settle at all, our differential settlement comes out to about 6mm.

Now, this number assumes the loaded side of the tank is free to settle while the unloaded side remains static. This is not the case. Assuming the tank is nice and stiff, some of the applied pressure on the loaded side will be transferred to the unloaded side (which will reduce the settlement of the loaded side).

I don't know what the application is for this tank, but the above is probably a pretty conservative analysis of the situation you described. I would be surprised if differential settlement potential turns out to be a problem for you.

EDIT: One thing to note is that the tank will "wiggle" when it is being filled/drained. What I mean is, the entire thing will settle more when it is filled, but it will settle more in the unloaded side (thereby undoing some of the differential settlement in the empty condition). Then when drained, the soil will rebound and the tank will return to the more-tilted empty condition when the unloaded side rebounds more than the loaded side (though it is likely neither side would rebound fully).

Assuming the 6mm of settlement from above, the deflection angle for the 24m diameter tank comes out to be $\arctan\frac{6mm}{24m}=0.014^{\circ}$. Pretty tiny.

• let's see if I get the units straight ... 80 pounds per cubic inch translates to 22MN/m³ reaction modulus? Would be in the ballpark of other numbers I seen. – mart Jan 29 '15 at 20:39
• yeah that would be a correct conversion. – Rick supports Monica Jan 29 '15 at 21:04