Between station 12+00 and station 30+00, a roadway grading plan shows 8{,}200 yd³ of excavation (bank measure) and 6{,}600 yd³ of embankment (compacted measure). The shrinkage factor from bank volume to compacted volume is 0.88. The change in the mass haul diagram ordinate across this interval, expressed in bank volume, is most nearly:
- (A)1{,}600 yd³
- (B)2{,}390 yd³
- (C)2{,}720 yd³
- (D)700 yd³
Show worked solution
Answer: (D)
Compacted fill converts to 6,600/0.88 = 7,500 yd³ of bank material, leaving a 700 yd³ cut surplus across the interval.
Cut and fill must be compared in the same measure, so bring the embankment to bank volume.
Surplus cut drives the ordinate upward: the change is cut minus fill, both in bank measure.
FE Reference Handbook — Civil Engineering: Earthwork Formulas (Shrinkage/Swell) and Mass Diagram
Why the other choices appear
- (A)Ignores shrinkage and subtracts volumes in different measures (8,200 − 6,600 = 1,600).
- (B)Multiplies the fill by 0.88 instead of dividing (8,200 − 6,600 × 0.88 = 2,392).
- (C)Applies the factor to the cut instead of the fill (8,200/0.88 − 6,600 = 2,718).