INTRODUCTION TO ENGINEERING SURVEYING

(CE 1305)

Sr Dr. Tan Liat Choon

Email: tanliatchoon@gmail.com

Mobile: 016-4975551

Levelling-Technical-1

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LEVELLING

TWO PEG TEST

Set 2 marks at 30-40 metre apart, also mark centre point in a relatively flat area

Set level at midpoint and take readings at each end

Determine difference in readings (difference in elevation)

Move level to one end and setup so that level is just in front of rod on point

Read rod by looking backward through scope (x-hair not visible), hold pencil on rod to determine reading

Read rod at other end in normal manner

Difference in readings should equal of 3

If values are not equal, there is error• Most instruments have adjustment screws• Adjust and repeat test as a check

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Two Peg Test

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L / 2 L / 2

xS1

S1’

Line of Collimation

Horizontal Line

L

AB

S2

S2’

x

L / 2 L / 2

x

S1

S1’

Line of Collimation

Horizontal Line

L

A

B

= S1’ - S2’

The APPARENT height difference δhA

The TRUE height difference hTδ

= S1 - S2

S1 = S1’ + x and S2 = S2’ + x 4

Two Peg Test

L / 2 L / 2

L

xS1

S1’

Line of Collimation

Horizontal Line

AB

S2

S2’

x

δThe TRUE height difference hT = S1’ - S2’

= S1 - S2The APPARENT height difference δhA

S1 = S1’ + x and S2 = S2’ + x hA = (S1’ + x) - (S2’ + x )δ 5

Two Peg Test

L / 2 L / 2

L

xS1

S1’

Line of Collimation

Horizontal Line

AB

S2

S2’

x

δThe TRUE height difference hT = S1’ - S2’

= S1 - S2The APPARENT height difference δhA

S1 = S1’ + x and S2 = S2’ + x hA = S1’ - S2’δ = δhT 6

Two Peg Test

hA δ = δhT

Therefore :

This is true since the instrument is the same distance from both staff positions and the errors x are equal and cancel out

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Two Peg Test

S3’

S3

AB

L / 10

Now move the instrument outside the “odd numbered” peg

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Two Peg Test

S3

S3’

AB

L / 10

S4

S4’

= S3 - S4The APPARENT height difference δ hA

δBut the TRUE height difference hT We already know

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Two Peg Test

S3

S3’

AB

L / 10

S4

S4’

= S3 - S4

= S1 - S2

then the instrument is OKIf NOT then the error is e =

The APPARENT height difference δ hA

δBut the TRUE height difference hT

δ δTherefore if hA = hT

(S1 - S2) - (S3 - S4) / L mm / m10

Two Peg Test

Summary Place two pegs about L = 30m (to 40m) apart

Set up level midway between the two pegs

Read staff on each peg, and calculate true height difference

Move level about L / 10 = 3m (or 4m) beyond one of the pegs

Read staff on each peg again, and calculate height difference

Collimation Error e = difference in the differencesand is expressed as a number of mm per L m

Acceptable errors

Uren and Price 1mm per 20m

Wimpey 4mm per 50m

Test should be carried out regularly say once per week or two11

L / 2 L / 2

L

S1

AB

S2

S3

AB

L / 10

S4

Collimation error,e = (S1 - S2) - (S3 - S4) mm / Lm

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DATUMCould be our own Datum - Assumed Datum

- Arbitrary Datum

- Site DatumOr

A National Datum

In the UK we have a national organisation known as The Ordnance Survey (O.S.)

The O.S. has established a ZERO Datum at Newlyn in Cornwall.

- Ordnance Datum

Based on the Ordnance Datum - points of known height aboveor below Zero height have been established around the U.K.

These points around the country are known as Bench Marks

Above Assumed Datum

Above Ordnance Datum

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Levelling

AB

Measured and CalculatedLevel of A

ReducedLevel of A

RL A (known)

ReducedLevel of B

RL B(unknown)

the Plane of CollimationHeight of

DATUM

(HPC)

HPC = RL A + S1

S1

Levelling Staff

HPC = RL A + S1

S2

RL B = HPC - S2

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A BC

Some Terminology

RL A RL BRL C

S1

Level staff on A Back Sight (BS) reading is first reading

BSLevelling

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RL A RL B

A BC

RL C

Level staff on A Back Sight (BS) reading is first reading

S2

Level staff on B Fore Sight (FS) reading is last reading

FS

Move instrument to new position

Levelling

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Move instrument to new position

RL A RL BRL C

A BC

Level staff stays on B

The instrument has changed its position about point B

Point B is known as a Change Point (CP)

CP

S3BS

2nd instrument position starts with BS to B

Levelling

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and finishes with

FS

FS to C

S4S3BS

RL A RL BRL C

A BC

Levelling

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RL A RL B

A BC

RL CBS FS

BS FS

RL A is knownHPC =

HPC

RL A + BS RL B = HPC - FS

RL B + BS RL C = HPC - FS HPC =

HPC

Generally : HPC = Known RL + Back SightUnknown RL = HPC - Fore Sight

(CP)

Now the RL B is known So we can repeat the process

Levelling

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PLANE AND COLLIMATION METHOD This method is simple and easy

Reduction of levels is easy

Visualization is not necessary regarding the nature of the ground

There is no check for intermediate sight readings

This method is generally used where more number of readings can be taken with less number of change points for constructional work and profile levelling

To check:

∑ BS - ∑ FS = Last RL – First RL

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PLANE AND COLLIMATION METHODDetermine the RLs of various points if the reduced level (RL) of a point on which the first reading was taken is 136.440 gives the Height of Plane and Collimation method and applies the check

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Station BS IS FS HLC RL Remarks12345

0.585

0.350

1.0101.7353.295

3.775

137.025

133.600

136.440136.015135.290133.730133.250

BM A RL=136.440

CPI678910 1.735

1.3001.7952.5753.375

3.895 131.440

132.300131.805131.025130.225129.705 CP 2

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0.6351.605

130.805129.835 BM B RL=129.835

Sum of BS=2.670 Sum of FS = 9.275

2.690-9.275 = -6.605 129.835-136.440= -6.605

HLC = RL + BS= 136.440 + 0.585 = 137.025RL = HL – BS

Check(Summation of BS)-(Summation of FS) = Last RL – First RL2.670 – 9.275 = 129.835 – 136.440-6.605 = -6.605

How Levelling is Conduct

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How Levelling is Conduct

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Calculation checks

∑ FS - ∑ BS = 1st RL - Last RL

∑ IS + ∑ FS + ∑ (RLs except first) = ∑ (each HPC x number of applications)

Check Misclosure

Allowable Misclosure = 5 √N mm. ("Rule of Thumb")

When calculations are checked and if the misclosure is allowable

Distribute the misclosure

Simple check

Full check

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RISE AND FALL METHOD This method is complicated and is not easy to carry out

Reduction of levels takes more time

Visualization is necessary regarding the nature of the ground

Complete check is there for all readings

This method is preferable for check levelling where number of change points is more

To check:

∑ BS - ∑ FS = ∑ Rise - ∑ Fall = Last RL – First RL

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RISE AND FALL METHODDetermine the RLs of various points if the reduced level (RL) of a point on which the first reading was taken is 122.156 gives the Height of Rise and Fall method and applies the check

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Station BS IS FS Rise Fall RL Remarks

1234

1.5360.974

1.1241.768

2.072

2.700

0.5360.7940.932

122.156121.620120.826119.894

BM A RL=122.156mCP1

CP2

56789

2.2361.4131.9941.6391.256

2.3621.3020.8740.8251.120

0.9340.5391.1690.519

1.238 118.656119.590120.129121.298121.817

CP 3CP 4CP 5CP 6CP 7

10 1.468 0.212 121.605 BM B RL=121.605

Sum of BS=12.172 Sum of FS =12.723

3.161 3.712

12.723-12.172=0.551 3.712-3.161=0.551 122.156-121.605=0.551

R/F = BS - FS= 1.536 – 2.072 = 0.536RL = HL – IS

Check(Summation of BS)-(Summation of FS) = Last RL – First RL12.172 – 12.725 = 121.605 – 122.156-0.551 = -0.551

How Levelling is Conduct

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COMPARISON

Plan and Collimation Method• Quicker

• Good for a lot of IFSs

Rise and Hall Method• More accurate

• More calculation

• Intermediate RLs are known

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ACCURACY IN LEVELLINGFor normal engineering works and site surveys

Allowance misclosure = ± 5 √ N mm

Where N = Number of instrument positions

OR

Allowance misclosure = ± 12 √ K mm

Where K = length of levelling circuit in KM

If actual misclosure > allowance misclosure, levelling should be repeated

If actual misclosure < allowance misclosure, misclosure should be equally distributed between the instrument positions

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CORRECTION IN LEVELLING

Correction = (Misclosure / No. of Station) x n, n+1, n+2 and ………

For example:

Loop 1 = (0.117 / 3) x 1 = 0.039m

Loop 2 = (0.117 / 3) x 2 = 0.078m

Loop 3 = (0.117 / 3) x 3 = 0.117m

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Example

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Example

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Example

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Example

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Example

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Example

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Example

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T H A N K YO UQ u e s t i o n & A n s w e r

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