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The following successive reading were taken with a level of 4m levelling staff on a continuously sloping ground at 15m interval.

1.500 (on P), 1.785, 2.490, 2.995, 3.555, 3.905, 0.600, 1.410, 2.510, 2.915, 3.105, 3.995, 0.960, 1.500, 1.675, 2.410, 2.995, 3.615( on Q)RL of P is 590.100m. Calculate the gradient of P Q.(HI Method)

1 Answer
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*after reading 3.905 next reading 0.600 is decrease and then increase 1.410

Then 0.600 is entered in FS and 1.410 enter on BS

Staff reading chainage B.S I.S F.S H.I R.L Remark
P 0 1.500 591.6 590.100 RL of BM
1 15 1.785 589.815
2 30 2.490 589.11
3 45 2.995 588.605
4 60 3.555 588.045
5 75 3.905 587.695
6 90 1.410 0.600 592.41 591 CP1
7 105 2.510 589.9
8 120 2.915 589.495
9 135 3.105 589.305
10 150 3.995 588.415
11 165 1.500 0.960 592.95 591.45 CP2
12 180 1.675 591.275
13 195 2.410 590.54
14 210 2.995 589.955
Q 225 3.615 589.335
∑B.S = 4.41 ∑F.S = 5.175

1. HI=RL of P + BS= 590.100 +1.500= 591.6

2. RL Of point 1= HI – IS of point 1 = 591.6 – 1.785 =598.815

3. RL Of point 2= HI – IS of point 2 = 591.6 – 2.490 =598.11

4. RL Of point 3= HI – IS of point 3 = 591.6 – 2.995 =588.605

5. RL Of point 4= HI – IS of point 4 = 591.6 – 3.555 =588.045

6. RL Of point 5= HI – IS of point 5 = 591.6 – 3.905 =587.695

7. RL Of point 6= HI – FS of point 6 = 591.6 – 0.600 =591

8. Change point= new HI of point 6= RL of point 6 + BS of point 6 = 591 – 1.410=592.41

9. RL Of point 7= HI point 6 – IS of point 7 = 591.6 – 2.510 =589.9

10. RL Of point 8= HI point 6 – IS of point 8 = 591.6 – 2.915 =589.495

11. RL Of point 9= HI point 6 – IS of point 9 = 591.6 – 3.105 =589.305

12. RL Of point 10= HI point 6 – IS of point 10 = 591.6 – 3.995 =588.415

13. RL Of point 11= HI point 6 – FS of point 11 = 591.6 – 0.960 =591.45

14. Change point= new HI of point 11= RL of point 11 + BS of point 11 =591.45– 1.500=592.95

15. RL Of point 12= HI point 11 – IS of point 12 = 592.95– 1.675=591.275

16. RL Of point 13= HI point 11 – IS of point 13 = 592.95– 2.410=590.54

17. RL Of point 12= HI point 11 – IS of point 14 = 592.95– 2.995=589.955

18. RL Of point Q= HI point 11 – FS of point Q = 592.95– 3.615=589.335

Arithmetic check:

∑B.S - ∑F.S = Last RL-First RL

4.41 - 5.175 = 589.335 – 590.100

-0.765 = -0.765

Gradient of PQ = (First RL-last RL) / (Distance PQ) = (590.100-589.335) / 225 = 1 / 294.12

= 1 in 294.12 (falling)

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