Earthwork

1. Earthwork Cross Section and Borrow Pit Methods

2. 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 881, and B-2 page 878 • Examples:26-1 and 26-3

3. Volumes • 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

4. 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). • End areas can be cut, fill, or transition (both). • Use the areas to compute volumes, knowing the distance between the sections. • The whole work can be done with photogrammetry and a computer software, or a total station

6. 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: 99.2 7.4 52 Elevation rod reading distance from CL

8. End Area Computation • Simple cases: formulae in fig 26-2, and fig26-4 • End areas by coordinates: we will learn it through (traversing)

10. End Area Computation • Simple cases: formulae in fig 27-2, and fig 27-4

11. 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.

12. Volume Computation • 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

14. Prismoidal Formula • 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

15. A2 = 0 Vp = (h/6) *{S2 + (4 S2/4) + 0 +} = (h/6) * 2 S2 = (h/3) S2 AM = (S/2)2 = S2/4 h S/2 A1 = S2 S

17. Volume Computation • 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.

18. Borrow-Pit Method • 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 4*27 • The idea is to multiply each height by the number of complete squares it is common to. ( )

20. 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 squares. 4- Compute the difference between the cut and the fill., pay attention to the expansion factor.

21. Site 1 Site 3 Site 2

22. PROJECT 1Instructions

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25. C D B A