451-102 Introduction to Surveying (BPD)
Download
Report
Transcript 451-102 Introduction to Surveying (BPD)
H.U. MINING ENGINEERING DEPARTMENT
MAD 256 – SURVEYING
LEVELING PROCEDURES
Equipment
•
•
•
•
•
•
Level
Tripod
Staff
Change plate
Staff bubble
50 m tape measure (sometimes)
What is levelling?
• A measurement process whereby the
difference in height between two or more
points can be determined
BS
FS
Difference in height
H=BS-FS
When do we level?
• Typical examples include :
To establish new vertical control (BM or TBM)
To determine the heights of discrete points
To provide spot heights or contours on a plan
To provide data for road cross-sections or volumes
of earthworks
To provide a level or inclined plane in the setting
out of construction works
Definitions
• Level surface
A surface over which water will not flow
The direction of gravity is always normal to a level
surface
• Horizontal surface
A horizontal surface will be tangent to a level
surface
Over short distances (<100 m) the horizontal
surface and the level surface will coincide
Definitions (cont.)
direction of gravity
horizontal
surface
level surface
limit of practical
coincidence (~100 m)
Reading an “E-face” staff
0.339
0.33
0.3
Collimation error
• Occurs when the line of sight (as defined by
the cross-hairs) is not horizontal
• Leads to an incorrect staff reading
error
horizontal line
More definitions
• Datum
A reference surface to which the heights of all
points in a survey or on a site are referred
May be arbitrary or a national height datum
In Australia we have the Australian Height Datum
(AHD)
The surface which defines the AHD is
(approximately) Mean Sea Level (MSL)
More definitions
• Reduced Level (RL)
The height of a point above the datum
• Benchmark (BM)
A stable reference point of known RL
Usually used as the starting and finishing point
when levelling
• Temporary Bench Mark (TBM)
A point placed (e.g. peg, nail, spike) to provide a
temporary reference point
More definitions
• Backsight (BS)
Always the first reading from a new instrument
station
• Foresight (FS)
Always the last reading from the current
instrument station
• Intermediate sight (IS)
Any sighting that is not a backsight or foresight
More definitions
• Change point (CP)
Location of the staff when the level is moved
Change points should be...
Stable
Well defined
Recoverable
e.g. sharp rock, nail, change plate, etc...
Rules for levelling
• Always commence and finish a level run on a
Benchmark (BM or TBM)
• Keep foresight and backsight distances as
equal as possible
• Keep lines of sight short (normally < 50m)
• Never read below 0.5m on a staff (refraction)
• Use stable, well defined change points
A sample loop
Setup 4
CP 3
BM A
Kerb
Setup 1
Setup 3
Kerb
Setup 2
CP 1
CP 2
Post
Booking the observations
CP 3
BM A
Back
Inter
Fore
BM A
1.32
3.98
Kerb
Setup 1
Kerb
CP 1
CP 2
Post
Point
CP 1
Booking the observations
CP 3
BM A
Back
Inter
Fore
1.32
BM A
3.98
2.56
Kerb
Setup 1
Kerb
CP 1
CP 2
Post
CP 1
1.25
Kerb
3.65
Post
0.67
Setup 2
Point
CP 2
Booking the observations
CP 3
BM A
Back
Inter
Fore
1.32
Setup 1
BM A
2.56
Kerb
Setup 3
Kerb
3.98
Kerb
3.65
Post
0.67
2.58
CP 2
Post
CP 2
Kerb
1.54
CP 1
CP 1
1.25
3.49
Setup 2
Point
CP 3
Booking the observations
Setup 4
CP 3
BM A
Back
Inter
Fore
1.32
Setup 1
BM A
2.56
Kerb
Setup 3
Kerb
3.98
Kerb
3.65
Post
CP 1
CP 2
Post
0.67
2.58
2.64
CP 1
1.25
3.49
Setup 2
Point
CP 2
Kerb
1.54
CP 3
3.79
BM A
Reducing levels (Rise and Fall)
Back
Inter
1.32
2.56
Fore
Fall
RL
50.00
3.49
Comment
3.98
BM A
CP 1
Kerb
0.67
Post
CP 2
Kerb
1.54
CP 3
3.79
BM A
1.25
3.65
2.58
2.64
Rise
Reducing levels (Rise and Fall)
Back
Inter
1.32
2.56
Fore
3.98
1.25
3.65
3.49
Fall
RL
2.66
50.00
47.34
Comment
BM A
CP 1
Kerb
0.67
Post
CP 2
Kerb
1.54
CP 3
3.79
BM A
2.58
2.64
Rise
Reducing levels (Rise and Fall)
Back
Inter
1.32
2.56
Fore
3.98
1.25
3.65
3.49
1.31
Fall
RL
2.66
50.00
47.34
48.65
Comment
BM A
CP 1
Kerb
0.67
Post
CP 2
Kerb
1.54
CP 3
3.79
BM A
2.58
2.64
Rise
Reducing levels (Rise and Fall)
Back
Inter
1.32
2.56
Fore
Fall
RL
2.66
50.00
47.34
48.65
BM A
CP 1
Kerb
2.40
46.25
0.67
Post
CP 2
Kerb
1.54
CP 3
3.79
BM A
3.98
1.25
3.65
3.49
1.31
2.58
2.64
Rise
Comment
Reducing levels (Rise and Fall)
Back
Inter
1.32
2.56
Fore
3.98
1.25
3.65
3.49
Fall
RL
2.66
50.00
47.34
48.65
BM A
CP 1
Kerb
46.25
49.23
Post
CP 2
Kerb
1.31
2.40
0.67
2.58
2.64
Rise
2.98
Comment
1.54
CP 3
3.79
BM A
Reducing levels (Rise and Fall)
Back
Inter
1.32
2.56
Fore
3.98
1.25
3.65
3.49
Fall
RL
2.66
50.00
47.34
48.65
BM A
CP 1
Kerb
46.25
49.23
50.14
Post
CP 2
Kerb
1.31
2.40
0.67
2.58
2.64
Rise
2.98
0.91
Comment
1.54
CP 3
3.79
BM A
Reducing levels (Rise and Fall)
Back
Inter
1.32
2.56
Fore
3.98
1.25
3.65
3.49
Fall
RL
2.66
50.00
47.34
48.65
BM A
CP 1
Kerb
Post
CP 2
Kerb
CP 3
1.31
2.40
0.67
2.98
0.91
46.25
49.23
50.14
1.54
1.04
51.18
2.58
2.64
Rise
3.79
Comment
BM A
Reducing levels (Rise and Fall)
Back
Inter
1.32
2.56
Fore
3.98
1.25
3.65
3.49
Fall
RL
2.66
50.00
47.34
48.65
BM A
CP 1
Kerb
Post
CP 2
Kerb
1.31
2.40
Comment
0.67
2.98
0.91
46.25
49.23
50.14
1.54
1.04
51.18
CP 3
50.03
BM A
2.58
2.64
Rise
3.79
1.15
Reducing levels (Rise and Fall)
Back
Inter
1.32
2.56
Fore
Rise
3.98
1.25
3.65
Fall
RL
2.66
50.00
47.34
48.65
BM A
CP 1
Kerb
Post
CP 2
Kerb
1.31
0.67
2.98
0.91
46.25
49.23
50.14
2.64
1.54
1.04
51.18
CP 3
50.03
10.01
3.79
9.98
BM A
3.49
2.40
Comment
2.58
1.15
Reducing levels (Rise and Fall)
Back
Inter
1.32
2.56
Fore
Rise
3.98
1.25
3.65
Fall
RL
2.66
50.00
47.34
48.65
BM A
CP 1
Kerb
Post
CP 2
Kerb
1.31
0.67
2.98
0.91
46.25
49.23
50.14
2.64
1.54
1.04
51.18
CP 3
50.03
10.01
3.79
9.98
(0.03)
BM A
3.49
2.40
Comment
2.58
1.15
Reducing levels (Rise and Fall)
Back
Inter
1.32
2.56
Fore
Rise
3.98
1.25
3.65
Fall
RL
2.66
50.00
47.34
48.65
BM A
CP 1
Kerb
Post
CP 2
Kerb
1.31
0.67
2.98
0.91
46.25
49.23
50.14
2.64
1.54
1.04
51.18
CP 3
50.03
10.01
3.79
9.98
(0.03)
BM A
3.49
2.40
Comment
2.58
6.24
1.15
6.21
Reducing levels (Rise and Fall)
Back
Inter
1.32
2.56
Fore
Rise
3.98
1.25
3.65
Fall
RL
2.66
50.00
47.34
48.65
BM A
CP 1
Kerb
Post
CP 2
Kerb
1.31
0.67
2.98
0.91
46.25
49.23
50.14
2.64
1.54
1.04
51.18
CP 3
50.03
10.01
3.79
9.98
(0.03)
BM A
3.49
2.40
Comment
2.58
6.24
1.15
6.21
(0.03)
Reducing levels (Rise and Fall)
Back
Inter
1.32
2.56
Fore
Rise
3.98
1.25
3.65
Fall
RL
2.66
50.00
47.34
48.65
BM A
CP 1
Kerb
Post
CP 2
Kerb
CP 3
1.31
0.67
2.98
0.91
46.25
49.23
50.14
2.64
1.54
1.04
51.18
10.01
3.79
9.98
(0.03)
6.24
1.15 50.03 BM A
6.21
(0.03) (0.03)
3.49
2.40
Comment
2.58
Reducing levels (Rise and Fall)
Back
Inter
1.32
2.56
Fore
Rise
3.98
1.25
3.65
Fall
RL
2.66
50.00
47.34
48.65
BM A
CP 1
Kerb
Post
CP 2
Kerb
1.31
0.67
2.98
0.91
46.25
49.23
50.14
2.64
1.54
1.04
51.18
CP 3
1.15
6.21
50.03
10.01
3.79
9.98
(0.03)
(0.03)
BM A
(Error)
3.49
2.40
Comment
2.58
(0.03)
6.24
Loop misclosure (Error)
• Misclosure (Error)
The amount by which the measured height
(RLmeasured) differs from the known height (RLknown)
of the starting and finishing benchmarks
Misclosure (Error) = RLmeasured – RLknown
Error = 50.03 – 50.00 = 0.03 m
or
Error = Back – Fore = 10.01-9.98 = 0.03 m
Error = Rise – Fall = 6.24-6.21 = 0.03 m
An acceptable misclose?
• Small misclosures in closed level loops are
expected because of the accumulation of
errors
• If the misclosure is small, it can be adjusted
• If the misclosure is large, the loop (or part of
it) must be repeated
• Misclosures can also result from errors in
published BM levels and from BM instability
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
Continuing the example
• The misclosure is +30 mm (0.03 m)
• The length of the loop is 0.7 km
• The misclosure limit is…
12(0.7) = ±10 mm
• The misclosure of +30 mm is too big
• The loop must be repeated (or find the error)
Adjusting the misclose
• Adjustment is carried out to ensure that the
measured and known RLs of the closing
benchmark agree
• The misclosure is linearly distributed
according to the number of set-ups
• The adjustment per set-up for the example is
Correction=(-0.03/4)
Adjusting the misclose
Measured RL Point
50.00
BM A
47.34
CP 1
48.65
Kerb
46.25
Post
49.23
CP 2
50.14
Kerb
51.18
CP 3
50.03
BM A
Correction
Corrected RL
Adjusting the misclose
Measured RL Point
Correction
Corrected RL
50.00
BM A
0.000
50.000
47.34
CP 1
-0.008
47.332
48.65
Kerb
46.25
Post
49.23
CP 2
50.14
Kerb
51.18
CP 3
50.03
BM A
=1*(-0.03/4)
Adjusting the misclose
Measured RL Point
Correction
Corrected RL
50.00
BM A
0.000
50.000
47.34
CP 1
-0.008
47.332
48.65
Kerb
-0.015
48.635
46.25
Post
-0.015
46.235
49.23
CP 2
-0.015
49.215
50.14
Kerb
51.18
CP 3
50.03
BM A
=2*(-0.03/4)
Adjusting the misclose
Measured RL Point
Correction
Corrected RL
50.00
BM A
-0.000
50.000
47.34
CP 1
-0.008
47.332
48.65
Kerb
-0.015
48.635
46.25
Post
-0.015
46.235
49.23
CP 2
-0.015
49.215
50.14
Kerb
-0.023
50.117
51.18
CP 3
-0.023
51.157
50.03
BM A
=3*(-0.03/4)
Adjusting the misclose
Measured RL Point
Correction
Corrected RL
50.00
BM A
0.000
50.000
47.34
CP 1
-0.008
47.332
48.65
Kerb
-0.015
48.635
46.25
Post
-0.015
46.235
49.23
CP 2
-0.015
49.215
50.14
Kerb
-0.023
51.18
CP 3
-0.023
50.03
BM A
-0.030
=4*(-0.03/4)
50.000
Adjusting the misclose
Measured RL Point
Correction
Corrected RL
50.00
BM A
-0.000
50.000
47.34
CP 1
-0.008
47.332
48.65
Kerb
-0.015
48.635
46.25
Post
-0.015
46.235
49.23
CP 2
-0.015
49.215
50.14
Kerb
-0.023
50.117
51.18
CP 3
-0.023
51.157
50.03
BM A
-0.030
50.000
Errors in levelling
• Collimation
• Parallax
• Change point instability
• Instrument instability
• Staff instability
• Benchmark instability
• Refraction
Errors in levelling
• Staff reading and interpolation errors
• Staff verticality
• Instrument shading
• Temperature on staff
• Booking errors (e.g. using just 1 benchmark)
• Earth curvature
• Magnetic field effects on auto level
Applications of levelling
•
•
•
•
•
•
Point heights (relative to a datum)
Height differences (independent of datum)
Longitudinal sections and cross sections
Data for volume calculations
Contouring
Setting out
Establishing a new point
New point
Benchmark
RLNEW
RLBM
Datum
Measuring height differences
H3
H2
Benchmark
H1
RLBM
Datum
Profiles and cross-sections
Benchmark
RLBM
Datum
Plotting contours
2.510
B
2.905
C
The RL’s for points A, B and C have been
determined by levelling. We are now
required to determine the location of the
contours using a 0.5 m contour interval.
1.100
A
Plotting contours
2.510
B
LINE AB
DHAB = 2.51 - 1.10 = 1.410
DAB = 10 m
For the 1.5 m contour:
D = 10*(1.5 – 1.1)/1.41 = 2.84
For the 2.0 m contour :
D = 10*(2.0 - 1.1)/1.41 = 6.38
B
For the 2.5 m contour :
D = 10*(2.5 - 1.1)/1.41 = 9.93
A
1.100
A
0.4
2.84
1.4
0.9
6.38
10 m
9.93
1.41
Plotting contours
2.510
B
2.905
C
LINE AC
DHAC = 2.905 - 1.100 = 1.805
DAC = 14.14 m
For the 1.5 m contour :
D = 14.14*(1.5 - 1.1)/1.805 = 3.13
For the 2.0 m contour :
D = 14.14*(2.0 - 1.1)/1.805 = 7.05
For the 2.5 m contour :
1.100
A
D = 14.14*(2.5 - 1.1)/1.805 = 10.97
Plotting contours
2.510
B
2.905
C
LINE BC
DHBC = 2.905 - 2.510 = 0.395
DBC = 10 m
no contours cross this line
1.100
A
Plotting contours
2.510
1.100
B
A
2.905
C