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INTRODUCTION TO ENGINEERING SURVEYING
(CE 1305)
Sr Dr. Tan Liat Choon
Email: [email protected]
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
1112
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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