The following readings in metres were obtained in levelling a section for a prop

Question

The following readings in metres were obtained in levelling a section for a proposed road, namely 4.32, 3.37, 1.15, 4.18, 1.72 and 4.48. The fourth and fifth readings were on a change point off the line of section. The remainder were at points 10m apart starting with the first reading at a point P, whose chainage is 1600 m and height above datum 39.82. Make up the level book and if the formation level at P is to be 40.78 and the rise 1 in 50, find the depth of earthworks at each 10m. (Ans: fill 0.96, fill 0.21, curt 1.81, All 4.18)

Explanation / Answer

First reading is at point P

Elevation of P above datum = 39.82m

Thus reduced level of P= 39.82 m

Staff reading at P= 4.32

Staff reading at Q= 3.37

Thus reduced level of Q= 39.82+4.32-3.37= 40.77

Reduced level at R= 40.77+ 3.37-1.15 = 42.99

Reduced level at S = 42.99+1.15-4.18 = 39.96

Staff reading backsight at S= 1.72

Reduced level at T = 39.96 +1.72-4.48 = 37.2

Now formation level at P = 40.78 but RL at P = 39.82 thus fill required =40.78-39.82 = 0.96

For a rise of 1 in 50 formation level at Q 10 m apart = 40.78+10/50= 40.98

Thus fill required = 40.98-40.77 = 0.21

Formation level at R= 40.78+ 20/50 = 41.18 thus cut required at R= 42.99- 41.18 = 1.81

Now point S is off the line of section

Thus formation level at T = 40.78+30/50= 41.38

Thus fill at T = 41.38-37.2 = 4.18

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