1. Long sections eg road cuttings Deep sections eg basement excavations
Volume methods
Long sections eg road cuttings
Deep sections eg basement excavations

2. D = distance between areas (Equidistance)
Consider a cutting for a proposed road
Area 5
Area 4
Area 3
Area 2
Area1

3. { + + } PRISMOIDAL METHOD (simpson’s rule) Odd number of areas
Cross-sectional areas at uniform intervals
Odd number of areas
4 x Sum of EVEN numbered areas
Sum of first and last areas
2 x Sum of ODD numbered areas
V = D { + + } 3

4. AVERAGE of first and last areas
END AREA METHOD (Trapezoidal Rule) Cross-sectional areas at uniform intervals +
AVERAGE of first and last areas {
SUM
of the other areas }
V = D
Where D = distance between areas (Equidistance)

5. Method of ‘Weighting’ A B C D E F G 1 2 3 4 5 6 ref w depth w x d A1 1 B1 A2 2 B2 3 C2 D2 E2 A3 B3 4 C3 A4 B4 C4 A5 B5 C5 D5 E5 F5 G5 A6 B6 C6 D6 E6 F6 G6
A B C D E F G 1 2 3 4 5 6