Question

In: Civil Engineering

Assume a trench 185’ long Assume trench has a width of 6' lnft Assume the trench...

Assume a trench 185’ long
Assume trench has a width of 6' lnft
Assume the trench is 17’ tall
Assume there is 36” pipe in the bottom
Assume the bedding is 21.6 cuyds
Assume sides are sloped at 1 to 1 and that the site falls with the pipe
Assume no shrinkage on the backfill
What is net volume of backfill in cubic yards?

Expert Solution

Hi,

Below is the solution of given problem.

To calculate the backfill volume we will follow the below steps:

Drawing a sketch of the trench
Calculation of total volume of trench in cubic yards
Calculation of volume of pipe in the trench
Calculation of back fill volume by deducting pipe and bedding volume from the total volume

Step 1

Drawing a sketch of the trench

A typical cross section sketch is attached below. Since there is a slope of 1:1 (1H:1V) on both sides, the top width will be bottom width +2 time of height= 6’+17’+17’ = 40’

Calculation of total volume of trench in cubic yards

Given Length (L) = 185’

Average Breadth (B) = (40’+6’)/2 = 23’

Depth = 17’

Total Volume of trench = 185’x23’x17’ = 72335 cubic feet

= 72335/9 cubic yard = 8037.22 cubic yard (1 cubic yard = 9 cubic feet)

Calculation of volume of pipe in the trench

Volume of Pipe = Length x Cross Sectional Area

Dia of pipe = 36 in = 36/12 feet = 3 feet

Volume of Pipe = 185’ x π/4 x 3’² = 1307.69 cubic feet

= 1307.69/9 cubic yard = 145.30 cubic yard

Calculation of back fill volume by deducting pipe and bedding volume from the total volume

Hence, total volume of backfill = total volume of trench –volume of pipe – volume of bedding

= 8037.22-145.30-21.6

=7870.32 cubic yards [Ans]

Hope the above meets the requirement.

Waiting to hear from you soon,

Warm Regards

Saras Jain

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