# (Solved Homework): STUDY THE CHART ABOVE IN GREAT DETAIL IT IS A PORTION OF THE…

STUDY THE CHART ABOVE IN GREAT DETAIL IT IS A PORTION OF THE MASS DIAGRAM SHOWN IN TABLE 3.3 OF THE TEXT For the purposes of the following 5 questions on this homework, at Station 4+00, let’s change the “End Area Fill (sy) to 1,000 sf. Now, what are the answers to the following questions for the revised Station 4+00? 1. Total Fill ccy? 2. Adjusted Fill bcy? 3. Algebraic Sum bcy) 4. Mass Ordinate? 5. What is the primary purpose of the Mass Diagram?

The change at Station 4+00 is:

End Area Fill = 1,000 sf.

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Let us start calculating the revised values for Station 4+00 with the new value of End Area Fill i.e. 1,000 sf.

1. Station 4+00

2. End Area Cut (sf) = 60 sf [Same as existing condition, no change]

3. End Area Fill (sf) = 1,000 sf [Changed from existing condition, earlier it was 600 sf]

4. Volume Cut (bcy) = (Average Area Cut between Stations)*(Distance Between Stations)

= (Average Area Cut between Station 4+00 & 3+00)*(Distance between Station 4+00 & 3+00)

= [(60+0)/2] sf * (400-300) f = 3,000 cf = 3,000/27 cy = 111 cy [Same as existing condition]

[1 Cubic Yard (cy) = 27 Cubic Feet (cf); hence accordingly conversion has been done in the above step.

5. Volume Fill (ccy) = (Average Area Fill between Stations)*(Distance Between Stations)

= (Average Area Fill between Station 4+00 & 3+00)*(Distance between Station 4+00 & 3+00)

= [(1000+1500)/2] sf * (400-300) f = 1,25,000 cf = 1,25,000/27 cy = 4,630 cy [new value for ccy]

[1 Cubic Yard (cy) = 27 Cubic Feet (cf); hence accordingly conversion has been done in the above step.

6. Stripping Cut (bcy) = 60 [Same as existing condition]

7. Stripping Fill (ccy) = 80 [Same as existing condition]

8. Total Cut (bcy) = Volume Cut – Stripping Cut = 111 – 60 = 51 [Same as existing condition]

9. Total Fill (ccy) = Volume Fill + Stripping Fill = 4,630 + 80 = 4,710 [New Value for Total Fill ccy –> Answer for Q. 1]

10. Adjust Fill (bcy) = Total Fill (ccy)/Shrinkage Factor = 4710/0.9 = 5,233 bcy [Answer for Q. 2]

11. Algebric Sum (bcy) = Total Cut (bcy) – Adjusted Fill (bcy) = (51 – 5233) = -5,182 bcy [Answer for Q. 3]

12. Mass Ordinate at Current Station = Mass Ordinate at previous station + Algebric Sum at Current Station

= -23,240 + (-5,182) = -28,422 [Answer for Q. 4]

1. Total Fill ccy = 4,710

2. Adjusted Fill bcy = 5,233

3. Algebric Sum bcy = -5,182

4. Mass Ordinate = -28,422

5. Primary Purpose of Mass Diagram –> Mass diagrams are used to determine the quantity of material moved and how far it can be moved. A mass diagram is a plot or graphical representation of the cumulative of Total Cut Volume & Total Fill Volume along an alignment. It also tells us about average haul, free haul and overhaul on a given segment of road.

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