6 minute solutions problem 3, Earthwork/Moisture Content

[clintonvillian]

The question is:

Compacted soil 5 ft deep is needed for a buildings 200' x 100' foundation. The soil will be borrowed from a loose bank. The borrow soil has a density of 120 lbs.cf, a water content of 7%, a shrink of 10% and swell of 12%.

The required Loose bank volume and contained water weight are?

A. 4120cy, 880,000 lbf

B. 4120cy, 977,000 lbf

C. 4610cy, 977,000 lbf

D. 4610cy, 1,050,000 lbf

My answer would be D. I would have gotten it wrong. (3703.7cy x 1.12)/(1-0.10) = 4610 CY I got that far...........

Then I thought you simply multiply 4610cy x 27cf/cy x 120lbs/cf x .07 = 1050000 lbf

There answer is C by using 4610cy x 27 x 120 x (.07/1.07). WHY???

 

[civilized_naah]

There is a defect (ambiguity) in the question. The specified density of 120 pcf is mentioned as the density of the borrow soil. But in what state? Embanked? or Loose? Since the question also states that soil is borrowed from a loose bank, we can assume that the expanded (loose) density is 120 pcf and not the bank density.

The final (compacted) volume is to be 100x200x5/27 = 3704 cy

The bank volume (in situ) is to be 3704/0.9 = 4115 cy

The loose volume is 4115x1.12 = 4609 cy

If the density in the loose condition is 120 pcf, then the total soil mass (solids+ water) = 14.93 million lb

In this condition, if the water content is 7%, then 7/107 fraction of the total weight is water. Thus, water weight = 976,947 lb

On the other hand, if the in situ density of the soil were 120 pcf, then the total soil mass (solids+ water) = 13.33 million lb

In this condition, if the water content is 7%, then 7/107 fraction of the total weight is water. Thus, water weight = 872,226 lb

 

[civilized_naah]

To answer the question about why not multiply by 0.07 and use the factor 7/107 instead, it is because of how the water content is defined. It is the ratio of the water weight to the SOLlDS weight. If you were to use the 0.07 multiplier, you would be considering the water content as the ration of the water weight to the TOTAL weight of the soil.

 

[clintonvillian]

Thanks! Makes more sense now. It is all in how the density is presented, whether or not it is the mass of solids or total mass!