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FHWA > NHI > TCCC > Tutorials > Drilled Shafts

Theoretical Volume - To calculate the theoretical volume of the shaft:

V=((πD²)/4)*L

EXAMPLE
Shaft Dia. = 36"
Shaft Length = 50'
Tip Elevation=+25.00 ft

((π36.0"²)/4)* (50.0')=

4072.03/4 = 1018.00 * 50.0' = 50,900/144 in² = 353,47 ft²/27 yd³ = 13.09 yd³ - Theoretical Volume

Divide by 144 to obtain square feet
Divide by 27 to obtain cubic yards

Return to Chapter 9

Data collection in table form

Truck Number	Volume of the truck in yd3	Depth to the top of the concrete measured from ref following each load	Elevation at top of concrete, following each load, based on Ref. elevation	Cumulative amount of concrete in hole following each load
Truck #	Volume per Truck yd3	Depth to Concrete (ft)	Conc. Elev. Ft.	Cuml. Conc. Yd3
1	9	51.2	+6.8	9.0
2	9	39.2	+18.8	18.0
3	9	22.0	+36.0	27.0
4	4	0.0	+58.0	31.0

Return to Chapter 9

Data collection in table form example

Assume the following shaft data;

Top of shaft elev.= +55.00
Shaft Dia. = 42"
Bottom of Shaft elev. = -20.00

Therefore, theoretical volume is:

(π(42.0")²)/4*(75.0')=

5542.48/4 = 1385.62 * 75.0'= 103921.5/144 in² = 721.67 ft²/27 yd³ = 26.72 yd³

Truck #	Volume per Truck yd3	Depth to Concrete (ft)	Conc. Elev. Ft.	Cuml. Conc. Yd3
1	9	48.7	+5.8	9.0
2	9	38.7	+16.3	18.0
3	9	26.0	+28.7	27.0
4	6	0.0	+55.0	33.0

Return to Chapter 9

Volume of a Shaft Equation and Example

Shaft diameter=D
Shaft length=L
π=3.142

V=(π(D²)/4)*L

Example:

D = 3'
L = 25'

V=(π(D²)/4)*L

V=3.142*9/4*25

V=28.28/4*25

V=7.07*25

V=176.75 ft³ or
176.75/27 = 6.55 cyds

Return to Appendix B

Volume of a Bell Equation and Example

h: height
R,r: radius of bases
V: volume
π=3.142

V= π(R²+rR+r²)h/3

Example

r = 1.5'
R = 4.5'
h= 5'

V= π(R²+rR+r²)h/3

V=3.142(20.25'+6.75'+2.25')5'/3

V=3.142(29.25)5/3

V=91.90*5/3

V=459.5/3

V=153.16 ft³ or
153.16/27=5.67 cyds

Return to Appendix B

Volume of a Toe of a Bell Equation and Example

h: height
R: radius of base
V: volume
π =3.142

V= πR²h

Example

h = 1'
R = 4.5'

V= πR²h

V=3.142*20.25*1

V=63.62*1

V=63.62 ft³ or
63.62 / 27=2.36 cyds

Return to Appendix B

Circumferences

D = diameter = 2 times R (radius)
π = 3.142

Circumference of Shaft (C) = πD

Circumference of Cage
C=π(D-2*req'd concrete cover)

Return to Appendix B