CIVL102 CIVL102  Surveying and Surveying Surveying and Surveying

CampCamp  

Basic Goal of SurveyingBasic Goal of Surveying

Obtain positions of built objects (3D)

Graphical representation of the Graphical representation of the results:results:

Paper form as a contour map

A plan at some suitable scale

Digital format (CAD)

Two Main Categories by sizeTwo Main Categories by size

1. Geodetic Surveying:

Large areas Considers curvature of the earth

Purposes:Purposes:

Determine figure of the earth (the “geoid”) and gravity field

Provide an accurate framework for a large survey

The GeoidThe Geoid Mean sea level (M.S.L.)

surface extended over the whole earth

Equipotential surface Perpendicular to direction of

gravity

Variations in the earth’s Variations in the earth’s mass distribution:mass distribution:

Geoid has irregular shape Cannot be mathematically

described in closed form.

Equatorial plane

Polar axisEllipsoid

Geoid

b

a

Equatorial plane

Polar axisEllipsoid

Geoid

b

a

Best-fitting Ellipsoid Model

Geodesists: often use the ellipsoid that best fits the geoid

Points on/ near earth surface: Given by geodetic latitude, longitude and height above ellipsoid

Fig. 1.1 The geoid (irregularities

greatly exaggerated)

Popular ellipsoid model: Popular ellipsoid model: Geodetic Reference System of 1980 (GRS80) Equatorial semi-axis a = 6378.1370 km; Polar semi-axis b = 6356.7523 km

Distortion inevitable when plotting a curved surface onto a flat map

Various map projection methods (mathematical geodesy)

Second Main Category by size:Second Main Category by size:

2. Plane Surveying

Relatively small areas Surface of the earth: “infinite horizontal plane”

Direction of gravity:Direction of gravity:

Constant over the entire site. Defines vertical lines ( “plumb lines”), Plane normal to a plumb line horizontal

plane.

Rectangular coordinate system: most suitable for plane surveying

For distance measurements: Flat earth assumption acceptable (up to 10 km 10 km) 10 km arc on earth surface: longer than subtended chord by < 10

mm

percentage error in length measurements: < 10/10000000 = 1 ppm (parts-per-million)

Laser instrument: typically error: 5 ppm Steel tape: no better than 100 ppm.

Plane surveying: suffices for all but the largest surveys Plane surveying: suffices for all but the largest surveys (for horizontal distances)(for horizontal distances)

Geodetic surveys: seldom performed by engineers in Geodetic surveys: seldom performed by engineers in private private

practicepractice

Types of Surveying Types of Surveying

Also classified by purpose - common types:

Topographic surveys

Determine locations & elevations of natural & constructed objects on the ground

For map making

Concerns all features of the landscape that can be shown for the particular map scale

Cadastral surveys

Determine lawful boundaries & areas of properties rather than detail features of the landscape

Used in legal disputes, taxation, etc.

Also called property surveys / boundary surveys

Engineering surveys

Surveying work for engineering projects before, during & after construction

E.g. setting out of tall buildings and dams; deformation monitoring after completion

Others:

Mining, hydrographic, highway, railroad, and tunnel surveys

In our course:

Mainly topographic and engineering surveying Implicit assumption:

Small sites Theory and techniques of plane surveying will

suffice

Note: Flat earth assumption may not hold for determination of

elevations

Tangent plane: deviates from spherical earth by

~ 2 m @ 5 km from point of tangency ~ 8 m @ 10 km (see Ex. 1.2).

Effects due to the earth’s curvature & remedies: Ch.2.

Survey results:Survey results: Often plotted on a plan True-to-scale representation of the area in a horizontal

plane

Measured: slope (inclined) distance

Plotted: horizontal projection

Height information conveyed on plan: use

Contour lines, or Spot levels (small “+”s with heights printed alongside)

Consider Fig. 1.2

Physical points A, B, and C

Essential information for Essential information for plotting:plotting:

Projections AB’ & AC’

In horizontal plane containing A (or any other horizontal plane)

A

C'B'

B

A' C

Fig. 1.2 Basic measurements in

surveying

5 basic quantities:

Slope distance AB, along with

Vertical angle B’AB (or zenith angle A’AB),

Horizontal distance AB’ = AB cos(BAB’)

Vertical distance B’B

Similar measurements: fix C relative to A,

Horizontal angle B’AC’ also needed to orient C relative to AB’ on the plot

A

C'B'

B

A' C

Fundamental techniques Fundamental techniques in surveyingin surveying

Other methods of measurementOther methods of measurement

Plan distance (e.g. AB’) by taping directly

Height difference (e.g. B’B, rise from A to B) by differential leveling (Ch. 2)

Detailed techniques: subsequent chapters.

Essential characteristic about surveying:Essential characteristic about surveying:

Before final details (such as C) can be surveyed: need reference points (e.g. A and B) to base the measurements on.

Control survey Control survey

Establish reference monuments Establish reference monuments ”Control points” Accuracy greatly affects final results Often run as first stage of survey project

Coordinate SystemsCoordinate Systems Coordinates to be calculated before plotting survey

results Use of appropriate coordinate system

Plane surveying:Plane surveying: Righted-handed, rectangular coordinate system x-y axes: on horizontal plane z-axis: // direction of gravity

Still need:Still need: Suitable origin and orientation

Based on physical entities

For For locallocal construction purposes: construction purposes:

An artificial system may suffice, e.g. choose convenient point “A” on site as origin

Usually assigned +ve (large) x, y coordinates -> all positive horizontal coordinates in the area

Point “B” picked relative to A Line AB (horizontal projection) defines “artificial

north”

AB often chosen // (or per.) to most building lines Height “0” (or other reference value) assigned to a

convenient point

All other coordinates calculated relative to these

Surveys over extended public areas:Surveys over extended public areas:

Often tied to an official coordinate system Primary level of control: from government authority

Official rectangular coordinate system: Official rectangular coordinate system: usually:usually:

x- and y-axes: directions of east and north Coordinates values along x, y axes: eastings (E) and

northings (N) Origin: usually in the country / region; assigned +ve

& large (E, N) all other horizontal coordinates positive

“0” of z-axis: often defined at mean sea level (M.S.L.)

Measuring angles and directions

Compass

Observe bearings

Used in reconnaissance and hasty work

Theodolite

A telescopic sight pivoted both horizontally & vertically

Built-in graduated circles for measuring horizontal & vertical angles

Angles: usually displayed in the /’/” system

2 radians = 360 (degrees); 1 = 60’ (minutes); 1’ = 60” (seconds)

Theodolites sold in Europe: g/c/cc system: angles in gons (or grads)

360 = 400g (gons); 1g = 100c; 1c = 100cc

Note: 50g79c98cc : conveniently expressed as 50.7998g

Theodolites used on construction sites: 20”, 6”, 5” or 3” of arc

Geodetic theodolites: 1” or even 0.1”

Optical theodolite & angle readings

Electronic theodolite with EDM mounted on top

Measuring lengths

Measuring tape Direct linear

measurements

Cheap

For small details

Fiberglass measuring tape

Steel tape

Electronic Distance Measurement (EDM)

Laser equipment for very accurate distance measurement

Measure up to thousands of meters with only a few mm’s error

Used in all serious control work, and often in detail surveys as well

EDM EDM & rechargeable battery

Measuring height differences:

Level & staff

Level: has telescope that can rotate about vertical axis, maintaining horizontal line of sight

Staff: long rod held vertically over point of interest, provides height readings to be read by the level

A pair of readings determines the change in height

Automatic Level Staff Readings ona staff

The tripod Three-legged stand with

pointed metal shoes Most surveying

instruments: mounted on top of tripods during use

Tripod legs: maneuvered to make instrument roughly horizontal & centered over the station marker, followed by fine adjustments on the instrument.

Surveying equipment mounted on a wooden tripod

More advanced instruments

Total station Theodolite, EDM, data

processor & display unit combined

Instant data conversion into 3-D coordinates

Interface with computers

Total station with memory cards

Aerial camera

Produces aerial photos for topographic, engineering, & cadastral surveys

Stereoscope

Used to view stereoscopic pairs of aerial photos; approximate heights of objects can be determined by stereoscopic viewing.

Global Positioning System (GPS)

Satellites-based systems giving accurate 3-D coordinates of point on earth occupied by a GPS receiver. Also used for navigation purposes

Computing tools Computers, plotters, spreadsheets & CAD: invaluable

tools for the surveyor

Saves hours of time & potential mistakes

Applications:

Automating long & routine calculations (Ch.2,4)

Least squares adjustment (Ch.1,2,3,4)

Graphical solutions (Ch.3,4,6)

Plotting thousands of points with little effort (Ch.5), etc.

Preliminaries, Planning, & General Preliminaries, Planning, & General

RulesRules

Any survey project:Any survey project:

Involves a series of measurements Errors accumulate

Fundamental principle of surveying:Fundamental principle of surveying:

Work from the whole to the part

1. Establish overall framework

Covering the whole area

Refined methods & instruments

Minimal number of points minimize error

Cheaper & quicker methods used meaningless for subsequent measurements

to be more precise than underlying framework

Carry out all measurements (& calculations) so that final product meets accuracy required by the purpose of survey

Suit the means to the end since accuracy is costly in speed & resources.

2. Fill in details based on accurate control framework