ES3D4 / ES4D5 Construction Management Surveying 1 Tony Price & Nikki Meads

ES3D4 / ES4D5 Construction Management

Surveying

1

Tony Price&

Nikki Meads


Surveying

• The main object of surveying is the preparation of maps or plans which are the basis in the planning and design of engineering projects such as route location, e.g. roads, railway lines, pipelines, tunnels, etc.


Classification of Surveys

• Surveying is divided into two main categories-i) Plane survey ii) Geodetic Survey


Geodetic Survey • Where a survey extends over a

large area greater than 200 sq. km. and the required degree of accuracy is also great.

• The curvature of earth is taken into account.

• Used to provide control points to which small surveys can be connected.

• Not common in Civil works.

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Plane Survey • For small projects

covering an area less than 200 sq.km.

• Earth’s curvature is not accounted for in distances. Earth surface is considered as a plane. (Angular error of 1” in 200 sq. km. area by assuming plane).

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Basic Principles in Surveying

• Ruling principles of surveying are :i) “ to work from whole to part”. For surveying you should establish control points of high precision by use of triangulation and precise levelling. This area is further divided into smaller triangles which are surveyed with less accuracy.ii) to fix the position of new stations by at least two independent processes – e.g. linear and angular


Setting-out• Whereas surveying maps the

existing world, setting-out establishes points for the control of construction processes, e.g.– Positioning foundations– Placing the line of a road or service– Controlling levels and gradients on

earthworks

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Health & Safety

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Health & Safety

Police said the surveyor was pinned beneath a 12-wheel truck Friday morning for more than an hour.

The truck was backing up when it struck the worker.

A 60-year-old man was taken to hospital with critical injuries. He was pronounced dead Friday afternoon.

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Health & SafetySurveyor electrocuted - Employer fined20 year old Surveyor Russell Donald died after

he was electrocuted passing under a high-voltage power line with a metal pole in Echt, Aberdeenshire. His employer, W A Fairhurst and Partner, has been fined £25,200.

The Glasgow based engineering firm were charged with failing to instruct Mr Donald that it was inappropriate to use a long surveying pole in the vicinity of electric lines.

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Principles of Measurements

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12



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Source of Errors• Personal Errors - no surveyor

has perfect senses of sight and touch

• Instrument Errors - devices cannot be manufactured perfectly, wear and tear and compatibility with other components

• Natural Errors - temperature, wind, moisture, magnetic variation, etc.

14


Systematic and Accidental Errors

• Systematic or Cumulative Errors -typically stays constant in sign and magnitude

• Accidental, Compensating, or Random Errors - the magnitude and direction of the error is beyond the control of the surveyor

• Gross Errors – operator stupidity?

15


Normal Distribution Curve

16

This is the target value


Precision

17


Accuracy & Precision

18


Accuracy and Precision• Better precision does not

necessarily mean better accuracy• In measuring distance, precision is

defined as:

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Standard Deviation

20

n

xx

n

v inii

ni

x

21

21

v

x

xi is an individual measurement

is the arithmetic mean (most probable value)

is a residual such that ii xxv


Standard Error

21

11

21

21

n

xx

n

vs i

nii

ni

x

v

x

xi is an individual measurement

is the arithmetic mean (most probable value)

is a residual such that ii xxv

(n-1) is known as the number of degrees of freedom or redundancy


Standard Error of Arithmetic Mean

22

Example: 30 m tape with a standard error of 6 mm. If we require a standard error of 3 mm on the distance measured, how many measurements are required?

n

63

n

ss xx

Giving n = 4


Probabilities Associated with the Normal Distribution

23

-1 s x_

+1 sx

_

-2 sx_

-3 sx_

+2 sx

_

+3 sx

_

Probability % Confidence interval

68.3 1

90.0 1.65

95.0 1.96

95.4 2

99.0 2.58

99.7 3

99.9 3.29

xsxsxs

xsxs

xsxs

Assumes normal distribution without gross or systematic errors


Example: Most Probable Value and Standard Error

24

Calculate the most probable value and its standard error.


Solution

25

The most probable value is given by the arithmetic mean as:


Solution cont.

26

Based upon the most probable value, the residuals and squares of these are calculated:


Solution cont.

27

Therefore the most probable value of the angle is:


Example : Distance

28

Calculate the most probable value for this distance, its standard error and confidence interval for a 95% probability.


Solution

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ES3D4 / ES4D5 Construction Management30

For 95% probability level the confidence interval for the true value is:

REJECT


Recalculate with remaining measurements:


Propagation of Standard Error

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Special law of propagation of standard error for a quantity U

2

2

2

2

2

2

2

1

2 ....21 nx

nxxU s

x

Us

x

Us

x

Us

D=a+b or a-b

A=xy

222baD sss

22222yxA sxsys


Example

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Converts “ to radians


Propagation of Errors

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Activity Standard Error

Levelling

Angular measurement

Trigonometrical heighting

Traversing

Dlss sH

Ss = standard error of reading staff; D = distance; l = sight length (foresight, backsight) Sm = std. error in angle reading; Sb = std. error bisecting target; n = number of measurements; SHA = std. error height of station A; Shi = std.error of height of total station above A; Shr = std.error of height of reflector above B; SL = std.error of slope length; Sa = std.error of angle;

nss

s bm22

2

222222222

sLsssss

LrhihAHBHcossin

nss aA


Example

37

If total station has a precision of 6” and targets and observers are such that Sb = 7.5” how many readings must be taken to achieve a precision of 5” in ?

nss

s bm22

2

Sm = 6, hence

n

222

5765

.

693.n

4 readings are required.


Levelling

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Profile Boards

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Define level

Define slope, e.g. on bank



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Closed Traverse

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N


What is a traverse?• A polygon of 2D (or 3D) vectors

• Sides are expressed as either polar coordinates (,d) or as rectangular coordinate differences (E,N)

• A traverse must either close on itself

• Or be measured between points with known rectangular coordinates

A closedtraverse A traverse between

known points


Rectangular coordinates

E=EB-EA

EA

NA

(EA,NA)

EB

NB (EB,NB)

Point A

Point B

North

East

N=NB-NA


Polar coordinates

d

North

East

Point A

Point B

~ whole-circle bearingd ~ distance


Whole circle bearingsBearing are measuredclockwise from NORTHand must lie in the range0o < 360o

North0o

East90o

South180o

West270o

1st quadrant

2nd quadrant3rd quadrant

4th quadrant


Coordinate conversions

22

1

NEd

NE

tan

cosdN

sindE

Rectangular to polar Polar to rectangular

d

E

N d

E

N


Applications of traversing

• Establishing coordinates for new points

(,d)

(,d)

(,d)

(E,N)new

(E,N)new

(E,N)known

(E,N)known


• These new points can then be used as a framework for mapping existing features

(,d

)

(,d) (,d

)(,d) (,d)

(,d)(E,N)new

(E,N)new

(E,N)new

(E,N)new

(E,N)new

(E,N)known

(E,N)known


• They can also be used as a basis for setting out new work

(E,N)new

(E,N)new

(E,N)known

(E,N)known


Equipment• Traversing requires :

– An instrument to measure angles (theodolite) or bearings (magnetic compass)

– An instrument to measure distances (EDM or tape)

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Measurement sequence• You start with a

known point and bearing AB

• At each station measure the internal horizontal angle

• Measure the vertical angle between each station

• Measure the distance between each station

ES3D4 / ES4D5 Construction ManagementES3D4 / ES4D5 Construction Management

• Whole circle bearing A to B: WCBAB

= 038° 17’ 34”• Point A has coordinates:

322.600E, 742.800N

• Sum of internal angles= (2n – 4)x90° = 720°because n = 6

114° 04’ 38”

090° 33’ 04”

083° 58’ 44”

237° 11’ 31”

088° 13’ 30”

105° 59’ 45”


Computation sequence1. Calculate angular misclosure

2. Adjust angular misclosure

3. Calculate adjusted bearings

4. Reduce distances for slope etc…

5. Compute (E, N) for each traverse line

6. Calculate linear misclosure

7. Adjust linear misclosure


Correction to anglesStatio

nAccepted Angle Correctio

nCorrected Angle

° ´ ´´ ´´ ° ´ ´´

A 114 04 38 -12 114 04 26

B 090 33 04 -12 090 32 52

C 083 58 44 -12 083 58 32

D 237 11 31 -12 237 11 19

E 088 13 30 -12 088 13 18

F 105 59 45 -12 105 59 33 720 01 12 720 00 00

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Correction = -72”/6 = -12” to each angle


Tape LengthsStations Proportional Error

betweenHorizontal distance

From To Out & back lengths (m)

A B 1:6100 90.202

B C 1:7020 86.756

C D 1:5010 48.928

D E 1:8230 69.187

E F 1:5930 57.345

F A 1:4930 108.784

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Bowditch adjustment• The adjustment to the easting

component of any traverse side is given by :

Eadj = Emisc * side length/total perimeter

• The adjustment to the northing component of any traverse side is given by :

Nadj = Nmisc * side length/total perimeter


Bowditch AdjustmentLineStnLine

Back B’gCorr’d Angle

Forward B’g

Horizdist

Unadjusted Correction Adjusted Coords

° ‘ “ E N E N E N E N

AB 038 17 34

A 114 04 26 322.600

742.800

AF 152 22 00 108.784

50.455 -96.375 0.021 -0.033 50.476 -96.408

FA 332 22 00

F 105 59 33 373.076 646.392

FE 078 21 33 57.345 56.166 11.571 0.011 -0.017 56.176 11.554

EF 258 21 33

E 088 13 18 429.252 657.946

ED 346 34 51 69.187 -16.056 67.298 0.013 -0.021 -16.043 67.277

DE 166 34 51

D 237 11 19 413.209 725.223

DC 043 46 10 48.928 33.846 35.332 0.009 -0.015 33.856 35.318

CD 223 46 10

C 083 58 32 447.065 760.541

CB 307 44 42 86.756 -68.602 53.108 0.016 -0.026 -68.585 53.082

BC 127 44 42

B 090 32 52 378.479 813.622

BA 090 32 52 90.202 -55.896 -70.795 0.017 -0.027 -55.879 -70.822

461.202

-0.087 0.138 0.000 0.000 322.600 742.800

59Checks

Knowns


Linear misclosure & accuracy

• Convert the rectangular misclosure components to polar coordinates

• Accuracy is given by

22

1

NEd

NE

tan

)/(: misclosurelinearlengthtraverse1

Beware of quadrant whencalculating using tan-1


N

E

b positiveadd 180o

Quadrants and tan function

+

b negativeadd 180o

+

b negativeadd 360o

+

+

b positiveokay


For the example…• Misclosure (E, N)

(-0.087, 0.138)

• Convert to polar (,d) = -032.23o (4th quadrant) = 327.77o d = 0.163 m

• Accuracy– 1:(461.202 / 0.163) = 1:2827


Curve Ranging

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Location Methods

(a) right angle offset tie.(b) the angle distance tie (polar tie).(c) angle at A and B of distance BP of AP

(intersection technique).

A

B

A A

B B

C PPP


Means of fixing a curve

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Establish line through ROr on line of radius. – How?

Locate position of pegs measuring angles at T from line to Q in combination with cord lengths T-1, 1-2, 2-3 and 3-4.

You cannot tape between 4 and 5 so how will you establish 5, 6 and 7?

ROr



67

R1

Method 1:

How far should R1 be from T?

ROr

Locate lines through the position of pegs 5, 6 and 7 by measuring angles at R1. Which direction should angles be read from and why?



68

R2

Method 2:R1

ROr


First line of sight marked by pegs and string

Second line of sight marked by pegs and string Point marked by peg and

nail at intersection of strings

Pegs must be firmly anchored in the ground

Documents

ES3D4 / ES4D5 Construction Management Surveying 1 Tony Price & Nikki Meads