A borrow source material, clayey silty sand, is proposed for the construction of a 150,000 yd$^3$ embankment fill. Lab results from the testing of the borrow source are:

- $ w = 9.3\% $
- $ Y_{\text{moist}} = 97.4 \, \text{lb/ft}^3 $
- $ \text{S.G.} = 2.65 $
- $ \text{LL} = 20 $
- $ \text{PI} = 5 $

The specifications require the embankment to be compacted to an in-place dry unit weight of 115 lb/ft$^3$ and $\pm 2\%$ optimum moisture content. Approximate the quantity of borrow required to construct the embankment.

A. 144,000 yd$^3$
B. 194,000 yd$^3$
C. 216,000 yd$^3$
D. 230,000 yd$^3$

The approximate quantity of borrow required to construct the embankment is approximately 15,960 yd³. The quantity of borrow refers to the amount of money or resources that are borrowed or taken on loan.

To calculate the quantity of borrow required to construct the embankment, we need to consider the dry unit weight and moisture content requirements.

1. Calculate the dry unit weight of the borrow material:
The specifications require an in-place dry unit weight of 115#/ft³. The lab result for the moist unit weight (Ymoist) is given as 97.4#/ft³. To find the dry unit weight (Ydry), we need to account for the moisture content (w).
Ydry = Ymoist / (1 + w/100)
Ydry = 97.4 / (1 + 9.3/100)
Ydry = 88.98#/ft³

2. Determine the moisture content range:
The specifications require the embankment to be compacted to an in-place dry unit weight within +/- 2% of the optimum moisture content. Since the moisture content is given as 9.3%, we need to calculate the range for the moisture content.
Moisture content range = +/- 2% of 9.3%
Moisture content range = 0.02 * 9.3
Moisture content range = 0.186%

3. Calculate the maximum and minimum dry unit weights:
Maximum dry unit weight = (1 + Moisture content range) * Ydry
Maximum dry unit weight = (1 + 0.186/100) * 88.98
Maximum dry unit weight = 89.154#/ft³

Minimum dry unit weight = (1 - Moisture content range) * Ydry
Minimum dry unit weight = (1 - 0.186/100) * 88.98
Minimum dry unit weight = 88.806#/ft³

4. Calculate the volume of borrow required:
Volume of borrow required = Embankment volume / (Maximum dry unit weight - Minimum dry unit weight)
Volume of borrow required = 150,000 / (89.154 - 88.806)
Volume of borrow required = 150,000 / 0.348
Volume of borrow required = 431,034.5 ft³

5. Convert the volume to cubic yards:
1 ft^3 = 0.037037 yd³
Volume of borrow required = 431,034.5 * 0.037037
Volume of borrow required = 15,960.33 yd³

Therefore, the approximate quantity of borrow required to construct the embankment is approximately 15,960 yd^3.

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