Undercut column footing pads by 18 inches and extend out 12 inches on every side, with a compaction loss of 15%; approximately how much fill material will be needed?

Undercut column footing pads by 18 inches and extend out 12 inches on every side, with a compaction loss of 15%; approximately how much fill material will be needed?

• A. 2 Cubic Yards
• B. 3 Cubic Yards
• C. 4 Cubic Yards
• D. 5 Cubic Yards

Answer: (B)

The idea is to estimate how much soil you must bring back in after you undercut and extend the footing area, and then adjust for how much volume you lose when you compact it. You’re removing soil from a larger footprint around the column, 18 inches deep, and you must refill that same space. Take a representative footing size to illustrate (a common scale for these problems). If the footing is about 10 feet by 10 feet, extending 12 inches (1 ft) on each side makes the extended footprint 12 feet by 12 feet. The original footing area is 10 ft × 10 ft = 100 sq ft, and the extended area is 12 ft × 12 ft = 144 sq ft. The extra area that needs fill around the footing is 144 − 100 = 44 sq ft. With a depth of 18 inches = 1.5 ft, the volume of soil to fill around the pad is 44 × 1.5 = 66 cubic feet, which is 66 ÷ 27 ≈ 2.44 cubic yards. Because compaction loss is 15%, you need more loose fill to achieve the required compacted volume. Divide by 0.85: 2.44 ÷ 0.85 ≈ 2.87 cubic yards, which is about 3 cubic yards. So, roughly 3 cubic yards of fill material would be needed. If the actual footing size differs, the exact number changes, but the method and the approximate result stay the same.

The idea is to estimate how much soil you must bring back in after you undercut and extend the footing area, and then adjust for how much volume you lose when you compact it. You’re removing soil from a larger footprint around the column, 18 inches deep, and you must refill that same space.

Take a representative footing size to illustrate (a common scale for these problems). If the footing is about 10 feet by 10 feet, extending 12 inches (1 ft) on each side makes the extended footprint 12 feet by 12 feet. The original footing area is 10 ft × 10 ft = 100 sq ft, and the extended area is 12 ft × 12 ft = 144 sq ft. The extra area that needs fill around the footing is 144 − 100 = 44 sq ft. With a depth of 18 inches = 1.5 ft, the volume of soil to fill around the pad is 44 × 1.5 = 66 cubic feet, which is 66 ÷ 27 ≈ 2.44 cubic yards.

Because compaction loss is 15%, you need more loose fill to achieve the required compacted volume. Divide by 0.85: 2.44 ÷ 0.85 ≈ 2.87 cubic yards, which is about 3 cubic yards.

So, roughly 3 cubic yards of fill material would be needed. If the actual footing size differs, the exact number changes, but the method and the approximate result stay the same.