FE 310 Lecture 19

Volumes / Earthwork

Types of volume determinations made by surveyors:

Methods of volume determinations:

Average End Area

10 + 12

10 + 80

A1

A2

HD = L

Formulas for end area

1. Level section

Example:

Roadbase = 18’

C 4.2

0

Sideslopes @ 1 ½ : 1

c

s

b

1

2. Three-level section

Example:

Roadbase = 18’

F7.4 F 6.3 F 4.9

23.1 0 20.4

c

b

hl

hr

dl dr

3. Five-level section

Example:

Roadbase = 18’

C11.4 C 8.6 C 4.3 C 2.7 C 1.5

26.2 20.3 0 20.1 24.4

b

fl

fr

dl dr

c

4. Areas for other irregular sections are found by triangles, planimeters or coordinates.

Volume by Average End Area

10 + 12

10 + 80

A1

A2

HD

272

21 Lx

AAV

Volume by Prismoidal formula

A prismoid is a solid whose ends are parallel and whose sides are plane or warped

surfaces

Where:

VP = Volume of the prismoid

A1 = Area of one cross section

AM = The area of a computed midsection

L = The horizontal distance between stations

Example:

Roadbase = 24’

Sideslopes are 1 ½ : 1

Station 15 + 00

F8.6 F 6.4 F 4.2

24.9 0 18.3

Station 16 + 00

F4.6 F 2.8 F 1.4

18.9 0 14.1

276

4 21

x

AAALV M

P

Step 1

Compute the midsection

Station 15 + 50

Step 2

Compute the end areas for all three

42

rlrl hhb

ddcarea

4

2.46.824

2

3.189.244.61area

..04.2151 ftsqarea

..20.822 ftsqarea

..03.144 ftsqareaM

Step 3

Compute the prismoidal volume

Solving this same problem by the average end area formula gives:

272

21 Lx

AAV