Plotting Mass Diagram

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Plotting Mass Diagram.— Figure 10-10 shows the values from the table of cumulative yardage plotted on a mass diagram. The vertical coordinates are cumulative volumes, plus or minus, from a line of line ofeach horizontal line representing an increment of 200 cubic yards. The horizontal coordinates are the stations, each vertical line representing a full 100-foot station.

As you can see, the mass diagram makes it possible for you to determine by inspection the yardage of cut or fill lying between any pair of stations. Between station 0 + 00 and station 3 + 50, for example, there are about 800 cubic yards of cut. Between station 3 + 50 and station 7 + 00, there are about 800 cubic yards of fill (descending curve). Between station 7 + 00 and station 10 + 50, there are about 850 cubic yards of fill (curve still descending), and so on.

Table 10-2.—Table of Cumulative Yardage

Figure 10-10.—Profile and mass diagram.

Remember that sections where the volume (yardage) changes from cut to fill correspond to a maximum in the mass diagram curve, and sections where it changes from fill to cut correspond to a minimum. The peaks and the lowest points of the mass diagram that represent the maximum or minimum yardage, occur at, or near, the grade line on the profile.

Balancing Cuts and Fills.— To understand the manner in which the mass diagram is used to balance cuts and fills and how haul limit is determined, let’s examine figure 10-10. Here the profile of a road, from stations 0 + 00 to 20 + 00, has been plotted above the mass diagram. You can see that they are plotted on the same horizontal scale. The labeled sections and arrows on the profile show relatively what is to be done to the cuts and fills; and where the limit of economical haul is exceeded, the cut is wasted, and the fill is borrowed. In figure 10-10, a 500-foot haul-limit line has been inserted into the mass diagram curve above and below the lines of zero yardage. (The 500-foot distance is laid out to scale horizontally parallel to the line of zero yardage.) The terminal points of these haul-limit distances were projected to the profile curve, as indicated. You can see that the cut lying between stations 1 + 00 and 3 + 50 can be hauled economically as far as station 6 + 00; that lying between stations 10 + 50 and 13 + 00, as far as station 8 + 00; and that lying between stations 14 + 00 and 16 + 50, as far as station 19 + 00. This leaves the cut between stations 0 + 00 and 1 + 00, the fill between stations 6 + 00 and 8 + 00, the cut between stations 13 + 00 and 14 + 00, and the fill between stations 19 + 00 and 20 + 00.

As indicated in figure 10-10, the cut between stations 0 + 00 and 1 + 00, lying outside the limit of economical haul distance, would be wasted; that is, dumped into a nearby spoil area or ravine. The cut between stations 1 + 00 and 3 + 50 would be dumped into the adjacent fill space between stations 3 + 50 and 6 + 00. The fill space between stations 6 + 00 and 8 + 00 would be filled with borrow; that is, material taken from a nearby borrow pit. The fill space between stations 8 + 00 and 10 + 50 would be filled with the cut between 10 + 50 and 13 + 00, and the space between stations 16 + 50 and 19 + 00 would be filled with the cut lying between stations 14 + 00 and 16 + 50. You will notice that the haul limit on the last section of the mass diagram (between stations 14 + 00 and 19 + 00) is almost on the line of zero yardage. This haul-limit distance also is called the balance line, because the volume of cut is equal to the volume of fill. If, for example, the balance line on the last section of the mass diagram in figure 10-10 is only about 400 feet, then instead of wasting the cut between stations 13 + 00 and 14 + 00, you would use that to fill the hollow between stations 19 + 00 and 20 + 00. Surplus cut remaining would naturally be wasted after allowing for shrinkage in the filled spaces.