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

economical haul distance is the mass diagram method.

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 the curve 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 the cost 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 over which 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.

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 stationsometimes 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.