Levelling 2

Levelling (continued)

This presentation covers booking, reduction, calculationchecks, actual and allowable misclosure and how we deal with an allowable misclosure.

TBM9.09 m A.A.D.

TBM10.00 m A.A.D.

Main Gate

Burnaby Building

Approximate North

Start at a TBM outside the main entrance of Burnaby Building and obtain the RL values of three points before closing onto another TBM near the main gate.

Point 1

Ground level at entrance to structures laboratory

Top of door level at entrance to structures laboratory

Site: …………………………………. Instrument: ………………………………….

Date: …………………………………. Observer: ………………………………….

Weather: …………………………………. Booker: ………………………………….

BS IS FS HPC RL Corr Corr RL Remarks

Burnaby Building L 52

07/10/98 M.A.R.

Good M.A.R.

TBM 10.00m AAD

It is important to complete details at the top of booking forms or on every page of field books.

TBM Level Posn. BS

Key

TBM CP Level Posn. BS FS

Key

Site: …………………………………. Instrument: ………………………………….

Date: …………………………………. Observer: ………………………………….

Weather: …………………………………. Booker: ………………………………….



07/10/98 M.A.R.

Good M.A.R.

TBM 10.00m AAD1.546 10.00011.546

C.P.

New staff position therefore a new row.

Each rowrepresentsa staffposition.

1.562

RL = HPC - FS RL = 11.546 - 1.562 = 9.984

9.984

After we make a FS and we have calculated the new RL we are finished with that instrument position.

Move the Instrument (about the CP) to a new position where we can see the CPand also the next point we want the RL value of.

TBM CP Level Posn. BS FS ISKey

Site: …………………………………. Instrument: ………………………………….

Date: …………………………………. Observer: ………………………………….

Weather: …………………………………. Booker: ………………………………….



07/10/98 M.A.R.

Good M.A.R.

TBM 10.00m AAD1.546 10.00011.546

C.P.1.562 9.9841.418

Same staff position as last reading therefore the same row

HPC = RL + BS HPC = 9.984 + 1.418 = 11.402

11.402


This reading is not the first so it is not a BSIt is not the last from this position (we can see the next points) so it is not a FSSo it is known as an INTERMEDIATE SIGHT (IS)

Site: …………………………………. Instrument: ………………………………….

Date: …………………………………. Observer: ………………………………….

Weather: …………………………………. Booker: ………………………………….



07/10/98 M.A.R.

Good M.A.R.

TBM 10.00m AAD1.546 10.00011.546

C.P.1.562 9.9841.418 11.402

Point 11.390

RL = HPC - IS RL = 11.402 - 1.390 = 10.012

10.012

New staff position therefore a new row

Site: …………………………………. Instrument: ………………………………….

Date: …………………………………. Observer: ………………………………….

Weather: …………………………………. Booker: ………………………………….



07/10/98 M.A.R.

Good M.A.R.

TBM 10.00m AAD1.546 10.00011.546

C.P.1.562 9.9841.418 11.402

Point 11.390 10.012

GL Struct. Lab Door


1.281

RL = HPC - IS RL = 11.402 - 1.281 = 10.121

10.121

Site: …………………………………. Instrument: ………………………………….

Date: …………………………………. Observer: ………………………………….

Weather: …………………………………. Booker: ………………………………….



07/10/98 M.A.R.

Good M.A.R.

TBM 10.00m AAD1.546 10.00011.546

C.P.1.562 9.9841.418 11.402

Point 11.390 10.012

GL Struct. Lab Door1.281 10.121

Top Struct. Lab Door


Requires an inverted staff i.e turn the staff upside down

Read and then book the staff with a negative sign

-2.420

The negative sign will keep all the calculations correct

RL = HPC - IS RL = 11.402 - (-2.420) = 11.402 + 2.420 = 13.822

13.822


The last point required is the TBM. However it is too long a sight.So we need a CP. This will be the last sighting from this positionTherefore a FS

Site: …………………………………. Instrument: ………………………………….

Date: …………………………………. Observer: ………………………………….

Weather: …………………………………. Booker: ………………………………….


07/10/98 M.A.R.

Good M.A.R.


Top Struct. Lab Door-2.420 13.822

TBM 10.00m AAD1.546 10.00011.546

C.P.1.562 9.9841.418 11.402

Point 11.390 10.012


CP New staff position therefore a new row

1.321

RL = HPC - FS RL = 11.402 - 1.321 = 10.081

10.081

Last Reading -- FS -- Move the instrument

Site: …………………………………. Instrument: ………………………………….

Date: …………………………………. Observer: ………………………………….

Weather: …………………………………. Booker: ………………………………….


07/10/98 M.A.R.

Good M.A.R.



TBM 10.00m AAD1.546 10.00011.546

C.P.1.562 9.9841.418 11.402

Point 11.390 10.012


CP1.321 10.0811.011 Same staff position as last reading therefore the same row

HPC = RL + BS HPC = 10.081 + 1.011 = 11.092

11.092

Site: …………………………………. Instrument: ………………………………….

Date: …………………………………. Observer: ………………………………….

Weather: …………………………………. Booker: ………………………………….


07/10/98 M.A.R.

Good M.A.R.



TBM 10.00m AAD1.546 10.00011.546

C.P.1.562 9.9841.418 11.402

Point 11.390 10.012


CP1.321 10.0811.011 11.092

TBM 9.09m AAD


2.007

RL = HPC - FS RL = 11.092 - 2.007 = 9.085

9.085


Before we look more fully at the results we will complete the second half of the levelling exercise


Top of door level at entrance to structures laboratory

Ground level at entrance to structures laboratory

Point 2

Site: …………………………………. Instrument: ………………………………….

Date: …………………………………. Observer: ………………………………….

Weather: …………………………………. Booker: ………………………………….


07/10/98 M.A.R.

Good M.A.R.



TBM 10.00m AAD1.546 10.00011.546

C.P.1.562 9.9841.418 11.402

Point 11.390 10.012


CP1.321 10.0811.011 11.092

TBM 9.09m AAD2.007 9.085

The RL value of 9.085m is our measured and calculated value.

It should be 9.09m. This gives an actual misclosure of 9.085 - 9.09 = -0.005m

This actual misclosure may be because of calculation errors or field errors

If it is due to calculation errors we MUST NOT continue.

Therefore the first thing we always do after reducing our field booking is:

Carry out Calculation Checks

FS - BS = 1st RL - Last RL

Simple Calculation Check:

Site: …………………………………. Instrument: ………………………………….

Date: …………………………………. Observer: ………………………………….

Weather: …………………………………. Booker: ………………………………….


07/10/98 M.A.R.

Good M.A.R.



TBM 10.00m AAD1.546 10.00011.546

C.P.1.562 9.9841.418 11.402

Point 11.390 10.012


CP1.321 10.0811.011 11.092

TBM 9.09m AAD2.007 9.085


3.975 4.890

LHS = 4.890 - 3.975 = 0.915 RHS = 10.000 - 9.085 = 0.915

Therefore LHS = RHS Therefore Calculations are OK

Site: …………………………………. Instrument: ………………………………….

Date: …………………………………. Observer: ………………………………….

Weather: …………………………………. Booker: ………………………………….


07/10/98 M.A.R.

Good M.A.R.



TBM 10.00m AAD1.546 10.00011.546

C.P.1.562 9.9841.418 11.402

Point 11.390 10.012


CP1.321 10.0811.011 11.092

TBM 9.09m AAD2.007 9.085

This Simple Check does not check the calculations for RL values calculated from IS

NOTCHECKED

NOTCHECKED

NOTCHECKED


3.975 4.890

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

Full Calculation Check:

1.418

1.546



TBM 10.00m AAD10.00011.546

C.P.1.562 9.98411.402

Point 11.390 10.012


CP1.321 10.0811.011 11.092

TBM 9.09m AAD2.007 9.085

LHS = IS + FS + (RLs except first) 0.251 4.890 63.105

= 0.251 + 4.890 + 63.105 = 68.246

RHS = (each HPC x number of applications) = (11.546x1 + 11.402x4

+ 11.092x1) = (11.546 + 45.608 + 11.092) = 68.246

Therefore LHS = RHS Therefore the calculations for all the RL values are correct.



TBM 10.00m AAD1.546 10.00011.546

C.P.1.562 9.9841.418 11.402

Point 11.390 10.012


CP1.321 10.0811.011 11.092

TBM 9.09m AAD2.007 9.085

Now we can look at the magnitude of the misclosure

We have already seen that the Actual misclosure = 9.085 - 9.09 = -0.005m Is this acceptable ?

Rule :

misclosure 12k mm, k = 563 mwhere k is the length of the loop in km

Therefore our Allowable misclosure say ± 9mm

Therefore Actual < Allowable Therefore our Fieldwork is OK

We have carried out the calculation checks and have an acceptable misclosure.

The final stage is to apply a correction procedure to distribute the actual misclosure.

We assume that we made a similar error every time we set up the instrument.

There are 3 backsights, so we set up the instrument 3 times.

We could divide 5 between 3 like this: 1 2 2 Or like this: 2 1 2

Let use choose the middle method. We will give 2mm to the 1st instrument position,an extra 1mm to the 2nd position, and an extra 2mm to the 3rd position.

The actual misclosure was -5mm, so we need to add 5mm in order to correct it.

We can add these 5mm to our Reduced Levels in any way, but it is best to assumethat the 5mm error occurred gradually as a set of small errors,

rather than all in one go.

We cannot divide our 5mm misclosure evenly between 3 positions, but we can do our best (we do not use fractions of a millimetre).

Or like this: 2 2 1

We must not correct the initial Reduced Level.

We apply the same correction to all readings up to and including each foresight.

Site: …………………………………. Instrument: ………………………………….

Date: …………………………………. Observer: ………………………………….

Weather: …………………………………. Booker: ………………………………….


07/10/98 M.A.R.

Good M.A.R.



TBM 10.00m AAD1.546 10.00011.546

C.P.1.562 9.9841.418 11.402

Point 11.390 10.012


CP1.321 10.0811.011 11.092

TBM 9.09m AAD2.007 9.085

xWe cannot correct the given TBM value

10.000

2

3

33

3

5

Corrections are applied with a +ve or -ve sign depending on the sign of the misclosure

9.986

10.015

10.124

13.825

10.084

9.09

We MUST end up with the correctfinal reduced level.

Calculation checks


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

Check Misclosure

Allowable Misclosure = 12 k mm.

When calculations are checked and if the misclosure is allowable

Distribute the misclosure.

Simple check

Full check

Loop misclosure

• Misclosure The amount by which the measured height

difference (Hmeas) differs from the known height difference derived from the RLs of the starting and finishing benchmarks (Hknown)

Misclosure = Hknown - Hmeas

Testing the misclose

• The amount of misclosure we are prepared to accept depends on the accuracy we are hoping to achieve

• For routine levelling, the third order levelling standard is adopted…

misclosure 12k mm

• where k is the length of the loop in km

Levelling 2

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Transcript of Levelling 2