Practice Question: Estimating Excavation Duration based on Equipment Productivity

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Solution

Excavation for the grade beam involves a trench with a bottom width of 3 feet, 1:1 side slope, and a depth of 4 feet, resulting in a top width (T):
\[T = 3 + 2(4 \times 1) = 11 \text{ ft}\]

The cross-sectional area of the trench is calculated as follows: 

\[A = \frac{1}{2}(3 + 11) \times 4 = 28 \text{ ft}^2\]

The perimeter of the building is determined by summing the lengths of its sides:
\[P = 200 + 140 + 80 + 20 + 15 + 70 + 25 + 70 + 80 + 160 = 860 \text{ ft}\]
or

\[P = 2 \times (200 + 160) + 2 \times 70 = 860 \text{ ft}\]

The volume of excavation is calculated as: 

\[V = 28 \times 860 = 24,080 \text{ ft}^3 \approx 892 \text{ yd}^3\]

The daily productivity, based on 12 cubic yards per hour and an 8-hour workday, is:

\[\text{Daily Productivity} = 12 \times 8 = 96 \text{ yd}^3/\text{day}\]

The estimated number of days required for excavation is given by: 

\[\frac{892}{96} \approx 9.3 \text{ days}\]

Accordingly the minimum number of days rounding up:

\[9.3 \text{ days} \rarr 10 \text{ days}\]

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