A project requires 2,400 cubic yards of fill material to be compacted to 95% Standard Proctor density. If the borrow material has a swell factor of 25%, how many cubic yards must be excavated?
Correct Answer
C) 3,000 cubic yards
With 95% compaction, you need 2,400 ÷ 0.95 = 2,526 cubic yards of loose material. With 25% swell: 2,526 × 1.25 = 3,157 cubic yards, closest to 3,000 cubic yards.
Why This Is the Correct Answer
Option C is correct because this problem requires a two-step calculation involving both compaction and swell factors. First, we must determine how much loose material is needed before compaction: 2,400 ÷ 0.95 = 2,526 cubic yards. Then we apply the swell factor to find the in-place excavation volume: 2,526 × 1.25 = 3,157 cubic yards. The closest answer is 3,000 cubic yards.
Why the Other Options Are Wrong
Option A: 1,920 cubic yards
Option A (1,920) represents applying only the compaction factor in reverse (2,400 × 0.80), but this ignores the swell factor entirely and uses an incorrect compaction calculation.
Option B: 2,280 cubic yards
Option B (2,280) appears to apply only a partial correction factor but doesn't properly account for both the compaction requirement and the swell factor in the correct sequence.
Option D: 3,800 cubic yards
Option D (3,800) overestimates the required excavation volume, possibly by applying the factors incorrectly or using wrong percentages in the calculation sequence.
Memory Technique
Remember 'CES': Compacted volume ÷ Compaction factor = loose volume, then × (1 + Swell factor) = Excavation volume needed.
Reference Hint
Look up earthwork calculations and soil volume change factors in construction management or site work chapters of your reference materials.
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