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How is the Buoyancy Reduction Factor Equation derived?

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Ocman76

Ocman76

Civil/Environmental
Mar 7, 2023
3
I have seen the following equation used in multiple engineering design manuals including AWWA M45, M55, and pipeline design books going back to the 90s.

Rb = Buoyancy Reduction Factor = 1 - 0.33 * Hw / H

Hw = groundwater height above buried pipe

H = depth of soil cover above buried pie

Usually this factor is used to determine the vertical dead load pressure on a buried pipe beneath a water table as follows:

Vertical Dead Load on pipe = Rb * γ * H

γ = soil unit weight

I'm struggling to understand how the buoyancy reduction factor is derived even though it is a simple equation. Google searches don't come up with anything as the results are all on buoyancy of objects immersed in water (not where the buoyancy reduction factor equation is used).

Any help is greatly appreciated!
 
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Seems to work if soil has a unit weight of 96 pcf
96-33 = 62.4 pcf = γw
In which case 0.33 * Hw/H * γs is the buoyant force

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."
 
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Right but that is a specific case which does not hold true for all soils. I have tried applying the buoyancy reduction factor equation to multiple different soils with different wet and dry densities and the results are always close to γS * H, but not the same. γS * H is the result of combining the water and saturated soil load on the pipe and simplifying:

Total vertical dead load on pipe = water pressure + weight of buoyant (saturated) soil = Hw * γW + H (γS - γW) = γS * H (when H = Hw).

If the buoyancy reduction factor formula is empirical why not just use the γS and γW to get a more accurate result for each specific soil?
 
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Right. That's what I do. No tricky equations can substitute for proper knowledge.

There is also a bouyant force acting on the pipe. 62.4 x pipe volume.


--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."
 
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I have just skimmed through this, but submerged soil is, in simple terms, slightly buoyant. if you just use Ys you are assuming that the item you are checking is always above the water table which is risky. Saturated soils will provide less downward force that unsaturated soils

Some codes insist on using the ground surface as your water table level as extreme rainfall could result in a period of completely saturated soil
 
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Slight difference. Submerged soil is not buoyant. It does not float.
The equation does not calculate buoyant force of a pipeline above or below the water table line; only the approximate total submerged weight of the soil above it. It ignores the pipeline completely, which must be entirely below the water table line. The submerged weight of the pipeline must still be calculated separately.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."
 
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Then it would not be submerged, wouldn't it.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."
 
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It can be pumiceous and still not quite float...it's not always 100% pumice. Altough the actual pumice does indeed float :)
 
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I know. In my yard I have bits of pumice and gasy rock that float and also tea pine, a wood with SG of about 0.95+ Stone that floats; wood that sinks.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."
 
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