ADVANCE SURVEYING

Areas from cross-sections Two-level section in filling

The same formula as derived above is applicable The same formula as derived above is applicable. Hence if b, h, n, m are given h1, h2, w1 and w2 can be computed and the area obtained as shown above.

Side hill two-level section From the geometry of Fig. below

From similar triangles HGF and FIC

Multilevel section Figure below shows a multilevel section where more than three levels are required to define the transverse slope of the ground. For a multilevel section the coordinate method of determining area is convenient. This has already been explained before.

FORMULAE FOR COMPUTATION OF VOLUMES 1- Volume by average end areas The volume by this method is given by =Average end areas x Length between the sections 2- Prismoidal Formula The volume is

Here Ao , A1 are the end areas where as M is the area of the middle section. 3- Volume by mean area method In this method the mean cross sectional area of the various sections is first computed as Volume V = Am X L where L is the length between the first and last section.

4- Trapezoidal rule for computing volumes If we have a series of sectional areas A1, A2……., Am at an equal interval of D, by end area methods

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