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Earthwork. Cross Section and Borrow Pit Methods. This lecture covers: Readings: 26-1 to 26-6, 26-8 to 26-10. Figures: 26-1 to 26-4, 26-6, and 26-7 Plate B-5 page 893, and B-2 page 890 Examples:26-1 and 26-3. Volumes. Usage: Quantities of earthwork and concrete

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Cross Section and Borrow Pit Methods

  • This lecture covers:

    • Readings: 26-1 to 26-6, 26-8 to 26-10.

    • Figures: 26-1 to 26-4, 26-6, and 26-7

    • Plate B-5 page 893, and B-2 page 890

    • Examples:26-1 and 26-3


  • Usage:

    • Quantities of earthwork and concrete

    • Capacities of some structures: tanks,..

    • Quantities of water discharged by streams per unit time

  • Units:

    • 1 yd3 = 27ft3

    • 1 m3 = 35.315ft3

    • Acre-foot: volume of an acre of 1 foot depth

The cross section method
The Cross Section Method

  • More accurate than a single profile along the centerline.

  • Done by measuring cross sections (profiles) at a right angles to the centerline, usually at intervals of 50, or 100 ft.

  • Readings at each cross section are taken at the centerline and at critical points perpendicular to the centerline.

  • Cross sections are drawn and design templates are superimposed, the difference in area is the area of cut or fill at that section (end area).

Data recording
Data Recording

  • Plate B-5

  • Left page looks like Profile leveling, no intermediate points

    • right page: in front of each station, a group of fractions that describe the point location, reading, and elevation, in the form:





rod reading

distance from CL

End area computation
End Area Computation

  • Simple cases: formulae in fig 26-2, and fig26-4

  • End areas by coordinates: we will learn it through (traversing)

End area computation1
End Area Computation

  • Simple cases: formulae in fig 27-2, and fig 27-4

compute individual areas and add them up. After computing the

elevation at critical points, form a table:(mistakes!)

station H L C D E R G

24+00 0 C12.5 C15.8 C18.0 C10.1 C12.2 0

15 15 33.8 20 0 33.3 15

Compute the areas and add them up.

Volume computation
Volume Computation the

  • Done after computing the end areas, identify which is cut and which is fill. Two main methods:

  • Average End Area: Multiply the average area of the two sections by the distance between them. See next slide

    • Ve = A1+ A2 * L yd3

      2 27

  • Prismoidal Formula the

  • What is a prismoid? A solid with parallel ends joined by a plane or continuously wrapped surfaces

  • Fits most earthwork problems

  • VP = L(A1+4AM+A2) yd3

  • 6*27

  • Where AM is the area of computed section midway between stations.

  • Prismodial Formula is more accurate, The difference is called CP: Prismoidal correction

Volume computation1
Volume Computation the

  • Compute end areas at stations, fill the first three columns in table 26-3.

  • Compute the cut and fill volumes, one of the formulae.

  • Multiply the fill volumes by an expansion factor.

  • Compute the amount of soil to be borrowed or transferred out of the site, which is the difference between the cut and the fill.

Borrow pit method
Borrow-Pit Method the

  • Not suitable for linear features, very useful for construction sites.

  • The site is divided into equal squares of sides 20,50, or a 100 ft. Elevations are then measured at the corners of the grid, which are given titles that correspond to the coordinates of the corner in the grid, ex: 3-D, 4-A,..

  • V =  (hijn) A yd3


  • The idea is to multiply each height by the number of complete squares it is common to.



The volume of any square, or part of a square is equal to the average

height(elevation difference) at the corners, times the area.

To compute the volume:

1- draw a line between the cut and the fill areas

2- compute the total volume

of all the complete cut squares,

do the same for the fill, use

the previous formula

3- Compute the

incomplete squares

separately and add them to the


4- Compute the difference

between the cut and the fill.,

pay attention to the expansion


Site 1 the average

Site 3

Site 2

Project 1 instructions
PROJECT 1 the average Instructions

36 the average

Assumed 36 for piles the average

200 ft

20 the average

C the average