Fundamentals of Transportation/Earthwork/Solution

 Problem: Given the end areas below, calculate the volumes of cut (in cubic meters) and fill between stations 0+00 and 1+50. Determine the true amount of excess cut or fill to be removed.


 * 0+00: Fill = 60
 * 0+50: Fill = 50
 * 0+75: Cut = 0, Fill = 25
 * 1+00: Cut = 10, Fill = 5
 * 1+15: Cut = 15, Fill = 0
 * 1+50: Cut = 30

 Solution: Two different methods need to be used here to compute earthwork volumes along the five strips. The average end area method can be used for non-zero sections. The pyramid method needs to be used for areas with zero ends.

For 0+00 to 0+50, use average end area:

$$Fill = \frac(50) = 2750\,\!$$

For 0+50 to 0+75, use average end area:

$$Fill = \frac(25) = 937.5\,\!$$

For 0+75 to 1+00, use the average end area method for the fill section and the pyramid method for the cut section:

$$Fill = \frac(25) = 375\,\!$$

$$Cut = \frac = 83.3\,\!$$

For 1+00 to 1+15, use the pyramid method for the fill section and the average end area method for the cut section:

$$Fill = \frac = 25\,\!$$

$$Cut = \frac(15) = 187.5\,\!$$

For 1+15 to 1+50, use the average end area method:

$$Cut = \frac(35) = 787.5\,\!$$

The sums of both cut and fill can be found:


 * Fill = 4087.5 cubic-meters
 * Cut = 1058.3 cubic-meters

Thus, 3029.2 cubic-meters of dirt are needed to meet the earthwork requirement for this project.

/Solutions