#76 The soil and the cost per cubic meter

The soil and the cost per cubic meter - Civil Engineering

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Free Chegg Question

A proposed embankment fill requires 3500 m3 of compacted soil. The void ratio of the compacted fill is specified as 0.65. Four borrow pits are available, as described in the following table, which lists the respective void ratios of the soil and the cost per cubic meter for moving the soil to the proposed construction site. Make the necessary calculations to select the pit from which the soil should be bought to minimize the cost. Assume Gs to be the same at all pits.

Borrow pit	Void ratio	Cost ($/m3)
A	0.85	9
B	1.2	6
C	0.95	7
D	0.75	10

Free Chegg Answer

Step 1

Find the dry unit weight  using the formula.
 â€¦â€¦ (1)
Here,  is specific gravity of soil solids,  is unit weight of water, and e is void ratio.
Substitute  for  and 0.65 for e.
 â€¦â€¦ (2)
Find the dry unit weight soil required for  compacted soil using Equation (2).

Thus, the volume of soil to be excavated from borrow pit is .
Find the dry unit weight of soil for borrow pit A using Equation (1).
Substitute  for  and 0.85 for e.

Similarly, calculate for borrow pit B, C, and D and tabulate the values in Table (1).

Step 2

Find the volume to be excavated (V) from the borrow pit A using the calculation.

Substitute  for .

Similarly, calculate for borrow pit B, C, and D and tabulate the values in Table (1).
Find the total cost for borrow pit A using the formula.

Substitute  for V and 9$ for cost.

Similarly, calculate for borrow pit B, C, and D and tabulate the values in Table (1).

Step 3

Tabulate dry unit weight, volume, and total cost for borrow pit A, B, C, and D as in Table (1).

Borrow pit	Void ratio (e)	at borrow pit		Cost	Total cost ($)
A	0.85		3926.2	9	35,335.8 $
B	1.2		4665.7	6	27,994.2 $
C	0.95		4128.8	7	28,959 $
D	0.75		3709.3	10	37,093 $

Thus, the  soil should be bought to minimize the cost.