A building requires 15,000 cubic feet of compacted fill. If the soil has a shrinkage factor of 20%, how many cubic feet of loose soil must be excavated?
Correct Answer
D) 18,750 cubic feet
With 20% shrinkage, the soil compacts to 80% of its loose volume. To get 15,000 CF compacted: 15,000 ÷ 0.80 = 18,750 cubic feet of loose soil needed.
Why This Is the Correct Answer
When soil is compacted, it shrinks to a smaller volume than its loose state. A 20% shrinkage factor means the compacted soil occupies only 80% of its original loose volume. To determine how much loose soil is needed to achieve 15,000 cubic feet of compacted fill, we must divide the required compacted volume by the compaction factor (0.80). This calculation accounts for the volume reduction that occurs during the compaction process.
Why the Other Options Are Wrong
Option A: 12,000 cubic feet
This answer incorrectly applies the shrinkage factor by subtracting 20% from the required compacted volume (15,000 × 0.80 = 12,000), which gives the wrong relationship between loose and compacted soil volumes.
Option B: 15,000 cubic feet
This answer assumes no volume change occurs during compaction, ignoring the 20% shrinkage factor entirely, which would result in insufficient compacted fill.
Option C: 18,000 cubic feet
This answer incorrectly adds 20% to the compacted volume (15,000 × 1.20 = 18,000), but this doesn't properly account for the compaction ratio relationship.
Memory Technique
Think 'Shrink to Divide' - when soil shrinks during compaction, you divide the final volume by the remaining percentage to find the starting volume needed.
Reference Hint
Look up soil compaction and earthwork calculations in the construction materials or site work sections of your reference manual.
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