As discussed previously, when you know the area of two cross sections,
you can multiply the average of those cross-sectional areas by the known
distance between them to obtain the volume of earth to be cut or filled.
Consider figure 10-9 that shows the plotted cross sections of two
sidehill sections. For this figure, when you multiply the average-end
area (in fill) and the average-end area (in cut) by the distance between
the two stations (100 feet), you obtain the estimated amount of cut and
fill between the stations. In this case, the amount of space that
requires filling is computed to be approximately 497.00 cubic yards and
the amount of cut is about 77.40 cubic yards.
MASS DIAGRAMS.—A concern of the highway designer is economy on earthwork. He wants to know exactly where, how far, and how much earth to move in a section of road. The ideal situation is to balance the cut and fill and limit the haul distance. A technique for balancing cut and fill and determining the
Figure 10-9.—Plots of two sidehill sections.
Figure 10-8.—Coordinates for cross-section station 305 shown in figure 10-7.
economical haul distance is the mass diagrammethod.
A mass diagram is a graph or curve on which the algebraic sums of cuts and fills are plotted against linear distance. Before these cuts and fills are tabulated, the swells and compaction factors are considered in computing the yardage. Earthwork that is in place will yield more yardage when excavated and less yardage when being compacted. An example of this is sand: 100 cubic yards in place yields 111 cubic yards loose and only 95 cubic yards when compacted. Table 10-1 lists conversion factors for various types of soils. These factors should be used when you are preparing a table of cumulative yardage for a mass diagram. Cuts are indicated by a rise in thecurve and are considered positive; fills are indicated by a drop in the curve and are considered negative. The yardage between any pair of stations can be determined by inspection. This feature makes the mass diagram a great help in the attempt to balance cuts and fills within the limits of economic haul.
The limit of economic haul is reached when thecost of haul and the cost of excavation become equal. Beyond that point it is cheaper to waste the cut from one place and to fill the adjacent hollow with material taken from a nearby borrow pit. The limit of economic haul will, of course, vary at different stations on the project, depending on the nature of the terrain, the availability of equipment, the type of material, accessibility, availability of manpower, and other considerations.
The term free-haul distance means a distance overwhich hauling material involves no extra cost. This distance is usually taken to be about 500 feet– meaning that it is only for hauls longer than 500 feet that the limits of economic haul need to be considered.
Table 10-1.—Soil Conversion Factors (Conversion Factors for Earth-Volume Change)
Tabulating Cumulative Yardage.—The first step in making a mass diagram is to prepare a table of cumulative yardage, like the one shown in table 10-2. Under End Areas, you put the cross-sectional area at each station—sometimes this is cut, sometimes fill, and sometimes (as at stations 9 + 00 and 15 + 00) part cut and part fill. Under Volumes, you put the volumes of cut or fill between stations, computed from the average end areas and the distance between sections in cubic yards. Note that, besides the sections at each full station, sections are taken at every plus where both the cut and the fill are zero. Note also that cut volumes are designated as plus and fill volumes as minus.
Under Algebraic Sums Volumes, Cumulative, you put the cumulative volume at each station and each plus, computed, in each case, by determining the algebraic sum of the volume at that station or plus and the preceding cumulative total; for example, at station 8 + 00 the cumulative total is –563. At station 9 + 00 there is a volume of cut of +65 and a volume of fill of –305, making a net of –240. The cumulative total at station 9 + 00, then, is (–563)+ (–240), or –803.