Question

A proposed embankment fill requires 7100 ft of compacted soil. The void ratio of the compacted fill is specified as 0.5. Four borrow pits are available as below, which list the respective void ratios of the soil and the cost per cubic feet for moving the soil to the proposed construction site. Make the necessary calculations to determine the total cost for each pit. Assume the specific gravity of soil solids, Gs to be the same at all pits.

1. Calculate the volume of solid (Vs) = ft3 Borrow Pit A: void ratio = 1.05 and the unit cost = $ 6 /ft3
2. Calculate the total cost to pay to Pit A = Borrow Pit B: void ratio = 0.61 and the unit cost = $ 7 /ft3
3. Calculate the total cost to pay to Pit B = Borrow Pit C: void ratio = 0.81 and the unit cost = $ 4 /ft3
4. Calculate the total cost to pay to Pit C = Borrow Pit D: void ratio = 0.73 and the unit cost = $6 /ft3
5. Calculate the total cost to pay to Pit D =

Answer 1

1) the volume of solid (Vs) is 4733.33 ft³

2) the total cost to pay Pit A is $58220

3) the total cost to pay to Pit B is $53344.67

4) the total cost to pay to Pit C is $34269.32

5) the total cost to pay to Pit D is $49132.02

Explanation:

given the data in the question;

Vs = ?, V = 7100 ft³, e = 0.5

1) Calculate the volume of solid (Vs)

Vs = V / ( 1 + e )

we substitute

Vs = 7100 / ( 1 + 0.5 )

Vs = 7100 / 1.5

Vs = 4733.33 ft³

Therefore, the volume of solid (Vs) is 4733.33 ft³

2) Calculate the total cost to pay to Pit A

VpitA / Vcomp = ( 1 + e
`_(PHA)`) / ( 1 + e
`_{comp` )

we substitute

VpitA / 7100 = ( 1 + 1.5) / ( 1 + 0.5)

VpitA / 7100 = 1.3666666

VpitA = 1.3666666 × 7100

VpitA = 9703.33 ft³

Total cost = volume × unit cost = 9703.33 ft³ × 6 = $58220

Therefore, the total cost to pay Pit A is $58220

3) Calculate the total cost to pay to Pit B = Borrow Pit C: void ratio = 0.81 and the unit cost = $ 4 /ft3

Vpitb / Vcomp = ( 1 + e
`_(PHB)`) / ( 1 + e
`_{comp` )

we substitute

VpitB / 7100 = ( 1 + 0.61) / ( 1 + 0.5)

VpitB / 7100 = 1.0733333

VpitB = 1.0733333 × 7100

VpitB = 7620.666 ft³

Total cost = volume × unit cost = 7620.666 × 7 = $53344.67

Therefore, the total cost to pay to Pit B is $53344.67

4) Calculate the total cost to pay to Pit C = Borrow Pit D: void ratio = 0.73 and the unit cost = $6 /ft3

VpitC / Vcomp = ( 1 + e
`_(PHC)`) / ( 1 + e
`_{comp` )

we substitute

VpitC / 7100 = ( 1 + 0.81) / ( 1 + 0.5)

VpitC / 7100 = 1.2066666

VpitC = 1.2066666× 7100

VpitC = 8567.33 ft³

Total cost = volume × unit cost = 8567.33 × 4 = $34269.32

Therefore, the total cost to pay to Pit C is $34269.32

5) Calculate the total cost to pay to Pit D

VpitD / Vcomp = ( 1 + e
`_(PHD)`) / ( 1 + e
`_{comp` )

we substitute

VpitD / 7100 = ( 1 + 0.73) / ( 1 + 0.5)

VpitD / 7100 = 1.1533333

VpitD = 1.1533333 × 7100

VpitD = 8188.67 ft³

Total cost = volume × unit cost = 8188.67 × 6 = $49132.02

Therefore, the total cost to pay to Pit D is $49132.02