METHOD OF LEVELLING - COMPUTING REDUCED LEVEL USING RISE AND FALL METHOD

COMPUTING REDUCED LEVEL USING RISE AND FALL METHOD

This method consists of determining the difference of level between consecutive points by comparing each point, after the first, with that immediately preceding it. The difference between their staff readings indicates rise or fall depending on whether the staff reading at the point is smaller or greater than that at the preceding point. The reduced level of each point is then found by adding the rise too, or subtracting the fall from, the reduced level of the preceding point.

It is to be noted that the terms ‘rise’ and ‘fall’ always refer to rise or fall from the first point to the second point, second point to the third point and not conversely.

The steps involved are as follows:

1. It consists of determining the difference of levels between the consecutive points by comparing their staff readings.

2. Obtain the rise or fall by calculating the difference between the consecutive staff readings. Rise is indicated if the back sight is more than the foresight, and a fall if the back sight is less than the foresight.

3. Find out the reduced levels of each point by adding the rise too, or by subtracting the fall from, the reduced level of the preceding point.

Check: ΣBS – ΣFS = ΣRise = ΣFall - Last RL - First RL

Station	BS	IS	FS	Rise	Fall
A	0.665
B		0.825			0.160
C		2.540			1.715
D	3.200		0.385	2.155
E	1.565		1.400	1.800
F		2.000			0.435
G			2.450		0.450

 

ΣBS = 5.430; ΣFS = 4.235; ΣRise = 3.955; ΣFall = 2.760

Here also the reduced level of the benchmark is assumed as 100.00 and the back sight to the benchmark is taken. Then the staff is held at B and reading recorded as intermediate sight.

RL of B = BM – Fall

(As the intermediate sight at B is greater than the back sight at A)

Then RL of C = RL of B – Fall of C (Fall of C = IS at C – IS at B)

Now there is a change point and so the back sight and foresight are to be taken, and as the intermediate sight (i.e., 2.540) is greater than foresight (i.e., 0.385) there is a rise.

Rise = 2.540 – 0.385 = 2.155

RL of D = RL of C + Rise = 98.125 + 2.155 = 100.280

Now there is another change point and here also, as the back sight (3.200) is greater than the F.S (1.400), there is a rise.

Rise = 3.200 – 1.400 = 1.800

RL of E = RL of D + Rise = 100.280 + 1.800 + 102.080

Intermediate sight is taken with the staff at F and here as the intermediate sight (i.e., 2.000) is greater than backsight (i.e., 1.565) there is a fall.

Fall = 2.000 – 1.565 = 0.435

RL of F = RL of E – Fall = 102.080 – 0.435 = 101.645

This procedure is repeated till the last point is reached and the usual checks are applied to assess the correctness of the calculations.

Check: ΣBS – ΣFS = ΣRise – ΣFall = Last RL – First RL = 1.195

Problem-1

Given are the levels recorded in a levelling book. Complete the levels using rise and fall method.

Station	BS	IS	FS	RISE	FALL	RL	Remarks
BM	3.10					193.62	BM
1		2.56
2		1.07
3	1.92		3.96				CP
4	1.20		0.67				CP
5		4.24
6	0.22		1.87				CP
7		3.03
8			1.41

 

Solution: The levels are computed as below using rise and fall method

Station	BS	IS	FS	RISE	FALL	RL	Remarks
BM	3.10					193.62	BM
1		2.56		0.54		194.16
2		1.07		1.49		195.65
3	1.92		3.96		2.89	192.76	CP
4	1.20		0.67	1.25		194.01	CP
5		4.24			3.04	190.97
6	0.22		1.87	2.37		193.34	CP
7		3.03			2.81	190.53
8			1.41	1.62		192.15
	Σ 6.44		Σ 7.91	Σ 7.27	Σ8.74

 

Check: ΣBS – ΣFS = Last RL – First RL = ΣRise – ΣFall

6.44 – 7.91 = –1.47, 192.15 – 193.62 = –1.47, 7.27 – 8.74 = –1.47

Hence checked.

 

Problem-2

Given are the levels recorded in a levelling book. Complete the levels using rise and fall method.

BS	IS	FS	RISE	FALL	RL	Remarks
3.39					23.10	BM
	2.81
	2.51
	2.22					CP
2.61		1.88
	2.32
	1.92
		1.54

 

Solution: The levels are computed as below using rise and fall method

BS	IS	FS	RISE	FALL	RL	Remarks
3.39					23.10	BM
	2.81		0.58		23.68
	2.51		0.30		23.98
	2.22		0.29		24.27
2.61		1.88	0.34		24.61	CP
	2.32		0.29		24.90
	1.92		0.40		25.30
		1.54	0.38		25.68
Σ6.00		Σ3.42	Σ2.58	Σ0

Check: ΣBS – ΣFS = Last RL – First RL = ΣRise – ΣFall

Σ6.00 – Σ3.42 = 2.58, 25.68 – 23.10 = 2.58, 2.58 – 0.00 = 2.58

Hence checked.

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