1. ADVANCE SURVEYING

2. Surveing marks for computation areas
INTERoduction
As we said in previous lecture based on survey marks boundaries the topic of this lecture is about areas from cross – sections
Surveyors or civil engineers are often required to compute volumes of earthwork either in cut or in fill when planning a highway system. To compute stockpiles of coat, gravel or other materials knowledge' of volume computation is required. There are basically three methods for this
(i) Cross section method,
(ii) Unit area or borrow pit method,
(iii) Contour area method.

3. Areas from cross-sections
This is employed for computation of volumes for highways, railways and canals. Here a series of cross sections are taken along the length of the line at regular intervals.
These are obtained by measurements in the field. They can also be obtained by photograrnmetry, the cross sections are plotted on a sheet and over the cross section design templates are superimposed. The difference in the two areas will be the amount of cut or fill. This is shown in Fig below

5. Areas from cross-sections
The following five types of cross sections generally occur in practice
1. Level Section
2. Two level Section.
3. Side hill two level Section.
4. Three level Section.
5. Multi level Section

6. While different formulae can be derived for different types of cross sections, it is useful if all the areas are derived by using one method only, i.e. by considering the figure as a closed traverse. The coordinate axes are the finished grade and the centre line of the cross section. The general formula for area is

8. Since for a cross section in earth work, Y coordinates of two points are zero, the computation will be shortened if the second equation is used.
Level section
Coordinates of A, B, C and D, from Fig, below:

10. The negative sign is immaterial and should be ignored.
Where: b is proposed width for the road, railway, canal …etc.
h is height of the design level, n is the side slope.
Example 1: Prepare a table of end areas versus depth of fill from 0 to 10 m by increments of 1 m for level sections 20 m wide level road bed and side slopes 2 to 1 Fig. below.

11. Solution
We have area = h(b + nh): Here b =10 m and n = 2. Hence
Area = h [20 + 2h]
The results are given in tabular from b

12. Two-level section in cutting

14. From the geometry of above Fig.

15. Area in terms of coordinates

16. w1& w2 is left and right width slope respectively
Example 2. An irrigation ditch is with b = 5 m and side slopes 2 to 1. Notes
giving distance from centre line and cut ordinates for stations and are c 0.8/4.2, C 1.0, C 1.2/5.1 and C 1/4.7, C 1.2, C 1.3/5.1. Draw the cross sections and compute area of sections

17. Solution

18. THANK YOU