SME
Construction Engineering
Earthwork and mass haul
Use this for “A cut has an end area of 42.5 m² at one station and 28 m² at the next, 20 m on. How much earth lies between them?”
Chart
Shaded: ∫ from 0 to 20 of A(x) dx = 705
Kept: 0 ≤ x ≤ 20; the rest of the curve is dashed
This is an example. Type your own values to start a new problem.
V (m³)
=
L (m)
×
(
A₁ (m²)
+
A₂ (m²)
)
2
Formulas
V
=
L
×
A₁
+
A₂
2
705
=
20
×
42.5 + 28
2
Assumptions
•
The end area changes in a straight line from one station to the next.
•
Both sections are all cut or all fill.
•
The method runs a little high against the prismoidal formula when the two ends differ a lot.
Step-by-step
WE KNOW
A₁ = 42.5 m², A₂ = 28 m², L = 20 m
FIND
volume (V)
Step 1 · Find volume (V)
Use V = L × (A₁ + A₂) ÷ 2
Average the two end areas and multiply by the distance between them: the trapezoid under the area line.
V
=
20
×
42.5 + 28
2
V
=
20
×
70.5
2
V
=
1,410
2
V
=
705
m³
Check
Put the numbers back in. Both sides should match.
705
=
20
×
42.5 + 28
2
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
More problem types
Bank, loose and compacted volumes
Use this for “705 m³ of bank earth swells 25% when dug and shrinks 10% when compacted. What are the loose and compacted volumes, and how many 12 m³ truck loads is it?”
Overhaul beyond free haul
Use this for “3200 m³ of earth is hauled an average of 450 m, with 150 m of free haul and overhaul paid at $0.85 per m³·sta. What does the overhaul cost?”