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NAVEDTRA 14337 Table 10-2: cumulative yardage of a 2,000-ft road and its mass diagram with a 500-ft free haul

Tool	Earthwork Volumes and Mass Haul
Source	Naval Education and Training Professional Development and Technology Center (1994). Engineering Aid 2. Nonresident Training Course NAVEDTRA 14337, U.S. Navy, Pensacola, FL. Chapter 10, Table 10-2 (table of cumulative yardage) and Figure 10-10 (profile and mass diagram with the 500-ft haul-limit lines); Department of the Army (1985). Construction Surveying. Field Manual FM 5-233, Washington, DC. Chapter 4 (areas) and chapter 3 (curves).
Level	Undergraduate

Problem

Cross sections of a road were taken at every 100-ft station from 0+00 to 20+00 and at the plus stations where the cut or the fill runs out (3+50, 9+08, 10+50, 15+07, 16+50); the cut and fill end areas are those of the manual's Table 10-2 (186 ft² of cut at 0+00 down to 0 at 3+50, 186 ft² of fill at 7+00, both cut and fill at 9+00, 14+00, 15+00 and 20+00). Compute the volumes between stations by the average-end-area formula in cubic yards, the cumulative-yardage column, the balance points of the mass diagram, and, with a free-haul distance of 500 ft, the free-haul and overhauled volumes and the overhaul in station-yards of each loop.

Inputs to Enter

26 stations 0+00 … 20+00 with the Table 10-2 end areas (cut 186, 65, 44, 22, 0 … ; fill 0 … 22, 44, 65, 186, 119, 46 …), average end area, fill factor 1.00 (no soil conversion, as in the table)
Free-haul distance 500 ft, overhaul rate 0.50 per station-yard (illustrative), no borrow cost (no limit of economic haul)

Open the Earthwork Volumes and Mass Haul tool (loaded with this example)

Answers

Volumes: 0+00 to 1+00 cut 100 (186 + 65)/2/27 = 464.8 yd³ (table +465); 1+00 to 2+00 201.9 (+202); 7+00 to 8+00 fill 564.8 (−563); every printed volume reproduced within 1 yd³ except the 15+07 fill, printed −8 where the arithmetic gives 2.9
Cumulative: +465, +667, +789, +809 at 3+50 (the first grade point), back to 0 at 7+00, −862 at 10+50, +491 at 16+50, −416 at 20+00 (exact arithmetic −408.2: the manual's rounding accumulates 7.8 yd³)
Balance points 0+00, 7+00, 13+99, 18+73; three closed loops (809 yd³ forward, 865 backward, 497 forward) and an open end with 408 yd³ of borrow
Loop 1: the 500-ft free-haul line fits at +465 from 1+00 to 6+00 (the line drawn in Figure 10-10), free haul 344 yd³, overhauled 465 yd³ with an average haul of 600 ft (centroids at 0+50 and 6+50), overhaul 465 station-yd; loop 2 overhaul 515 station-yd; loop 3 (474 ft) all free haul; total 980 station-yd
Totals: cut 2,611 yd³, fill 3,019 yd³, net deficit 408 yd³

Notes

The tool's default inputs are this table; press Submit. Switch the sub-tool select to see the FM 5-233 chord-definition curve (PI 18+00, I 45°, D 15°: R 383.07, T 158.67, L 300.00, E 31.56, M 29.16, LC 293.19 ft, PC 16+41.33, PT 19+41.33), its Figure 3-20 sag curve (−10 % to +5 %, 600 ft, PVI 90+00 at 50.00: V_m 11.25, low point 91+00 at 60.00, second differences 2.50) and the manual's station 305 cross section (coordinate area 540.3 ft², three-level formula 507.71 ft²). The haul numbers come from the tool's exact piecewise-linear treatment of the ordinate checked by scipy (test_earthwork_volumes.php); the manual draws the line by eye and wastes and borrows the ends of its first two loops instead of overhauling.