Earthwork for Canals and Roads

Depending upon the terrain, alignment of canal or road and the proposed formation/bed level, the nature of earthwork will be either in cutting or in filling or partially in cutting and filling. Filling is called banking or embankment. Principles of conveying earth (lead and lift) and earthwork in different types of soils are the same as for earthwork excavation in foundation as described in Section. 

In order that the excavated or the banked sections remain without collapsing, side slopes depending upon the nature of the soil (angle of repose) are provided. Therefore, most cross-sections (except in rocks) are trapezoidal in geometry. 

The quantity of excavation or banking can be computed by using various mensuration techniques out of which three are given below : 

1. Mid-section Area Method, 
2. Mean Sectional Area Method or Trapezoidal Method, and 
3. Primordial Method. 

Note : Use of tabular statement is advocated for calculation of earthwork using any of the three methods. 

Mid-section Area Method 

In this method, the mean depth is to be calculated first by averaging the depth of two consecutive sections, From the mean depth, the area of the mid-section is to be worked out and the volume of earthwork to be computed by multiplying the area of mid-section by the distance between the two original sections. 

Volume of earthwork = Am x L 

where,       Am  = area of mid-section, and 

                    L  = length of distance between two consecutive sections. 

Referring to Figure, 

                                 (d1+ d2) 

we get,  dm =     ----------------------------

                                       2 

Am = Area of mid-section + area of two sides = Bdm + Sdm^2 

Therefore,  V = (Bdm + sdm^2) x L 

Mean Sectional Area Method or Trapezoidal Method 

This method is based on the assumption that the mid area of a pyramid is half the average area of the ends and the end sections are in parallel planes. If A1 and A2 are the areas of the ends and L is the length between two sections, the volume of the prismoid is given by 

                                    V =  (L/2)(A1+A2) or V= L X A, 

where,  A,  = mid-sectional area. 

Considering a number of consecutive sections, having areas Al, A2, . . . ,  An-1, An. 

Therefore, the total volume of earthwork = (L/2) (Al + 2A2 + 2A3  + . . . +2An-1 + An)

Prismoidal Method 

From mensuration, volume of a prism having end faces that are in parallel planes 

V = (L/6)(A1+A2+4Am)

where A1 and 42 are the cross-sectional areas at the ends of a portion of embankment or cutting of length L and A, is the mid-sectional area.