Volume methods

1
Volume methods

1. Long sections eg road cuttings
2. 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 (simpsons rule)

• Cross-sectional areas at uniform intervals
• Odd number of areas

4 x Sum of EVEN numbered areas
2 x Sum of ODD numbered areas
Sum of first and last areas

V D



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