els levelling

8/10/2019 ELS Levelling

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Elementary Land Surveying ELS_Levelling05_06: 1

Levelling

Principleoperation required in the determination ofheights of points on the surface of the Earth


Equipment

1. Level with tripod (deviceto gives a trulyhorizontal line)

2. Levelling staff (a suitablygraduated staff for

reading vertical heights)3. Chain/Tape (to enable

the points leveled to belocated relative to eachother on a map)

4. Change plate (staff baseplate)

5. Staff bubble


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Elements of Surveyors Level

1. TelescopeDiaphragm plane glass onwhich a series of line isetched (cross-hairs)Parallax in focusing the realimage formed by theobjective lens is made to lie inthe same plane as diaphragm

Procedure of focusing:

a) Adjusting eyepiece to bringdiaphragm into sharp focusb) Adjust focusing screw until no

parallax


Elements of Surveyors Level

2. Compensating Device in Automatic LevelThe telescope need onlybe approximatelylevelled and then a

compensating devicecorrects for the residualmislevelment


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Levelling Staff

1. Sectional and assembledby slotting onto oneanother vertically

2. Made of aluminium alloy3. E-shaped graduation

(reading to 1mm forordinary levelling)


Precision Levelling Staff

1. Used for moreaccurate work(accuracy to 0.1mm inuse with precise level)

2. Spring-mounted at the

top3. Made of invar alloy

(iron + nickel) whichhas a lower coefficientof expansion unaffected bytemperature effects


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Levelling Terminology

1. Level line is a surfacewhich is at a constantheight relative to MeanSea Level (MSL) and is acurved line

2. Horizontal line istangential to the levelline at any particularpoint and isperpendicular to the

direction of gravity.Over short distance, the 2

lines are taken tocoincide


Levelling Terminology (cont)

3. Datum A level line is chosen in which the elevation ofall points is referred

a) Mean Sea Level (MSL) is the mean of tidal

height over a period of time (> 19 years)b) Principal Datum Hong Kong (PDHK) most of

the works in HK refer to this. It is 1.230mbelow MSL (revised in June 1984)

c) Chart Datum (CD) is a tidal datum for marineworks and navigation


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Relationship among different datums(Source: Lands Department, No Date)



4) Bench MarksPoints of knownelevation above PDHK

a) Bench Mark (BM) established on verticalsurfaces such as wallsof buildings orsubstantial structures


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4. Bench Marks (cont)b) Temporary Bench Marks

(TBM) constructed atlocations on site or offsite, where the level ofthe mark is calculatedfrom PDHK

5. Reduced Level (RL) the height of a pointrelative to PDHK

6. Height of Collimation isthe height of collimationabove PDHK

+5.00

TBM

+10.00



7. Backsight (BS) 1 st sight taken after the level has been set up. It isalso a sight taken to a point whose height above HKPD is known

8. Foresight (FS) last sight taken before moving the level. It is also asight taken to a point whose height is required to carry on the lineof levels

9. Intermediate Sight (IS) other staff readings taken between BS and

FS10. Change Point (CP) the staff position at which a FS and then a BS

readings are taken

BS FS IS

CP


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BS

BS

FS

FS

ISIS


Field Procedure

1. The level is set up at P where BM may be observed andreadings taken at points A, B, C and Da) The 1 st reading (BS) made with the staff on a point of known

RLb) The staff is now held at points A, B and C (ISs) in turn, and

record the readingsc) A change point (CP) is chosen at D, owing to the nature of the

ground and take the reading (FS)


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Field Procedure (cont)

2. The staff remains at point D. The level is moved to Q, set up andlevelleda) Taking the reading on the staff at the change point D (BS)b) Followed by IS with the staff on E, F and G until a further change

becomes necessary3. This procedure is repeated until all the required levels have been

obtained4. The final staff position is at a point of known RL


Procedure in Levelling

1. Height of Collimation Method1st find the height of the line of collimation above the datum

Height of collimation (HC) = 128.480 + 3.222 = 131.702m PDa) level at B (rise from A to B)

= height of collimation reading at B = 131.702 1.414= 130.288m PD

b) level at B (rise from A to B)= height of collimation reading at B = 131.702 3.484= 128.218m PD


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Procedure in Levelling

2. Rise and Fall MethodRise 2 nd reading < 1 st readingFall - 2 nd reading > 1 st reading

a) from A to B

1st reading 2 nd reading= 3.222 1.414 = 1.808 (rise)level at B (rise from A to B)= level at A + rise= 128.480 + 1.808= 130.288mPD

b) from A to B

1st reading 2 nd reading= 3.222 3.484 = -0.262 (fall)level at B (fall from A to B)= level at A - fall= 128.480 + 0.262= 128.218mPD


Booking and Calculation

1.2191.2191.219

98.7601.8602.231

99.9791.8603.0792.2313.450

G99.9790.5720.646

F99.4071.0521.218

E98.3550.5172.270

D (CP)97.8380.4321.5852.787

C98.2700.1451.153

B98.4150.9381.008

A97.4771.2831.946

BM98.7600.663

RemarksRLFallRiseFSISBS

1) Rise and Fall Method each reading is entered on a different line in theappropriate column, except at a change point, where a FS and BS occupy thesame line. To check, BS - FS = Rise - Fall = Last RL First RL


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Booking and Calculation (cont)2) Height of Collimation Method the collimation height is obtained byadding the staff reading, which must be a BS, to the known RL of the point onwhich the staff stands. To check, BS - FS = Last RL First RL

1.2191.219

98.7602.231

99.9792.2313.450

G99.9790.646

F99.4071.218

E98.3552.270

D (CP)97.838100.6251.5852.787

C98.2701.153

B98.4151.008

A97.4771.946

BM98.76099.4230.663

RemarksRLCollimationFSISBS


Comparison

Rise and Fall MethodMore accurateMore calculationIntermediate RLs are known

Height of Collimation MethodQuickerGood for a lot of ISs


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Accuracy in Levelling

For normal engineering works and site surveys Allowable misclosure = 5 n mmwhere n = no. of instrument positions

OR Allowable misclosure = 12 k mmwhere k = length of levelling circuit in km

If actual misclosure > allowable misclosure,

levelling should be repeatedIf actual misclosure < allowable misclosure,misclosure should be equally distributed equallybetween the instrument positions


Summary of Levelling Fieldwork

For levelling fieldwork, the following practice should beadhered to in order to improve the accuracy of thelevelling works.

1. Levelling should always start and finish at points ofknown RL so that misclosure can be detected

2. Where possible, all sight lengths should be below 60 m3. The staff must be held vertically by suitable use of a

bracket bubble4. BS FS Lengths5. Reading should be booked immediately after they

are observed. Important readings, particularly readingsat change points, should be checked

6. The rise and fall method of reduction should be used ifpossible, especially for control works


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Collimation Error

if level is set up, levelled and the line of sight orcollimation is not truly horizontal, it will sweep out acone as it is rotated.this cone will be either above or below the horizontalplane

Level

Staff

Horizontal Line

Line of Sight


Permanent Adjustment Two Peg Test

1. On fairly level ground, set 2 points A and B, a maximum of 60mapart. Let this distance be L metres

2. Set up the level exactly midway between the points at point C andlevel carefully

3. Place a levelling staff at each peg in turn and obtain readings S1and S2S1 S2 = (S1 + x ) (S2 + x) = S1 S2

= true difference on height between A and BX is the error due to collimation error (inclination of the collimation line by

angle


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4. Move the level so that it is L/10 metres from point B atD. Take readings S3 and S4

Apparent difference in height between A and B = S3 S4If there is any difference between the apparent and true value,e = (S1 S2) (S3 S4) m per L metres(e should be less than 0.5mm per 10 m for average precision)



5. Any error e of the level should be adjusted using theadjusting screw with the collimation line altered to thecorrect staff readingFor example, to adjust the level with instrument at Dand staff at A,

S4 = S4 e(L/10 + L) / L6. The test should be repeated to ensure that the

adjustment has been successful


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Two Peg Test - Example

The reading obtained from a two-peg testcarried out on an automatic level with a singlelevelling staff set up alternately at 2 pegs A andB placed 60m apart are as follows:

1. With the level midway between A and BStaff reading at A = 1.283mStaff reading at B = 0.860m

2. With the level positioned 5 m from peg B onthe line produced from AB

Staff reading at A = 1.612mStaff reading at B = 1.219m

Find the collimation error (e) and correctedstaff reading (S4)?


Errors in Levelling

Errors in Equipment1. Collimation Error

Keep sight distance roughly equalCheck by two peg test regularly

2. Parallax Error

Move eye with respect to eyepiece, see if any relative movementbetween target & cross-hairs, if so adjust eyepiece

3. Defects of Staff Zero error, check by tape, does not affect height difference if onestaff is used3-section staff should be properly extended

4. TripodRobust, properly tightenedOn soft ground, force it firmly into the ground


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Errors in Levelling (cont)

Field Errors1. Staff not vertical

Staff is held vertical with aid of a bracket bubble

2. Unstable ground A change plate should be used

3. Instrument not levelEnsure that the circular bubble is centered before and after areading is taken

4. Weather condition Avoid windy condition Avoid line of collimation close to the ground in hot weather

5. CheckingStart and finish at points of known heightRun a loop


Errors in Levelling (cont)

Reading and Booking Errors1. Misreading of the staff graduation

Keep sight distance < 60 m, otherwise it becomesimpossible to take accurate readings

2. Erroneous BookingCarefully entered the reading into the fieldbook always read the staff, book the observation and thencheck that the recorded entry agrees with a secondreading through the telescope.


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Error adjustments in levelling calculations



-0.008-0.008-0.008

32.6402.1314.433

32.6322.1312.1234.4334.425

BM32.6400.00832.6321.2980.816

CH10031.3390.00531.3340.5720.7752.114

CH8030.7670.00530.7620.1241.347

CH6030.8910.00530.8860.8561.223

CH4031.7450.00331.7420.8332.8420.367CH2032.5780.00332.5750.3182.009

CH032.8960.00332.8930.2531.691

BM32.640-32.6401.944

RemarksCorrected

RLCorrectionProvisional

RLFallRiseFSISBS

1. Rise and Fall Method


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-0.008-0.008

32.6404.433

32.6324.4334.425

BM32.6400.00832.6320.816

CH10031.3390.00531.33433.4480.7752.114

CH8030.7670.00530.7621.347

CH6030.8910.00530.8861.223

CH4031.7450.00331.74232.1092.8420.367

CH2032.5780.00332.5752.009

CH032.8960.00332.8931.691

BM32.640-32.64034.5841.944

RemarksCorrected

RLCorrectionProvisional RLCollimationFSISBS

2. Height of Collimation Method



Note:Misclosures = -0.008mNo. of instrument station = 3Correction is +0.0027m and is added to the RL foundfrom each instrument stationNo adjustment is applied to the initial BM, since thislevel cannot be altered.


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Additional Levelling Methods

1. Inverted Staff Used to determine the RL ofpoints, such as the soffit of abridge, underpass or canopyThe inverted staff reading isbooked with a negative sign

-4.100-4.100-4.100

72.30013.0001.640

68.20013.0008.9001.640-2.460

D) Kerb68.2008.4104.200

C) Canopy76.6104.050-2.560-4.210

B) Floor Level72.5604.5901.490

A) Frame (lift-shaft)77.1504.850-3.100

BM72.3001.750



Example

0.4100.4100.410

30.0002.4900.148

30.4102.4902.9000.1480.558

B30.4102.4901.383

Arch soffit32.9000.233-1.107

Top of wall32.6672.667-1.235-0.874

TBM A30.0001.432


0.4100.410

30.0000.148

30.4100.1480.558

B30.4101.383

Arch soffit32.900-1.107

Top of wall32.66731.793-1.235-0.874

TBM A30.00031.4321.432

RemarksRLCollimationFSISBS


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Additional Levelling Methods

2. Reciprocal LevellingBy means of reciprocal levelling, the need for applyingcurvature and refraction corrections may be avoided2 similar instruments in correct adjustment are requiredH = ((a1 b1) + (a2 b2)) / 2


Example

In levelling across a river, reciprocal levellingobservations gave the following results for staffsheld vertically at X and Y from level stations Aand B on each bank respectively:

Staff reading of X from A = 1.753mStaff reading of X from B = 2.080mStaff reading of Y from A = 2.550mStaff reading of Y from B = 2.895m

If the RL of X is 90.370m PD, calculate the RL ofstation Y.(note: Y is lower than X)


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Effects of Earths Curvature and Atmospheric Refraction

A. Earths CurvatureIn ,

L2 + R 2 = (R + c) 2

L2 = (R + c) 2 - R 2

L2 = 2cR + c 2

L2 2cR c L2 / 2R (km)

= 0.0785 L 2 (m)whereradius of the Earth,

R 6370 kmand L in km


Effects of Earths Curvature and Atmospheric Refraction

RefractionLine of sight is not really horizontal and bentdownwards towards the Earth

Value not constant, affected by pressure, temperature,latitude, humidity etc.Usually taken as 1/7 and opposite of the correction ofcurvature

Combined correction= 0.0785 L 2 * (6/7) = 0.0673 L 2 (m)

where L in kmIf L = 120m, c = -0.00097m 0.001m 1mmThe effect is negligible for ordinary levelling


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Example

A staff is held at a distance of 200m from a leveland a reading of 2.758m obtained. Calculate thereading corrected for curvature and refraction.

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