Surveying CE 341 Eng. Mysa.A.AL- Khassawneh Jordan university Of science and technology.

Surveying CE 341

Eng. Mysa.A.AL-Khassawneh

Jordan university Of science and technology

Surveying:The science that deals with earth measurements

Values could be :Measured: using instruments contain errorsComputed: no instrumented needed no errors

Instrument: human operation environmental effect (temp) errorMeasurement: direct: Angles height , point positing indirect: area , volume, surfaces , contour maps

Measurement categorization :Linear: length width height ( elevation or altitude)Non linear:Angles ( horizontal and vertical)Surface in 3D

Type of surveying:1.Control survey:Establish a network of horizontal and vertical monuments that serves a reference framework for initiating other surveys2. Topographic survey:Determine locations of natural and artificial features and elevations used in map making3. Boundary (property) surveying Establish property lines and property corner markers

4. Hydrographic surveys :Define shoreline and depths of lakes, streams , oceans, reservoirs, and other bodies of water5. Rout surveying :Surveying used to plan, design and construction high ways , railroads, pipelines, and other linear projects ( different alternatives for the hwy)6. Construction survey:Provide base line, grade, control elevations, horizontal positions, dimensions for construction operations( pay quantities)

Construction surveying:

7. Engineering surveying:Laying out and construction of different engineering projects such as highways, dams buildings…..8. Inventory survey:Population density, forest areas, zonation….

Branches of surveying1. Plane surveying horizontal plane x-y neglect curvature of the earth suitable for a small area and short

lines(r<10 miles)2. Geodesy : -consider the curvature of the

earth(sphere) - applicable for large area ,long lines

3. GIS: geographic information system link a data base to a map4. GPS: global positioning systemObtain (x,y,z) for point

5. Remote sensing:Qualitative (color intensity)Recognition of classificationSpacing image

Theory of measurement:Type of measurements in surveying:There are five measurement in plane surveying:1.horizontal distance2.Horizontal angles3.Vertical distances4.Vertical angles5.Slops distances

Error, types and magnitude of error in measurements:True error in a measurement:It is the difference between the measured value of a parameter and its true value ei = xi-xWhere :ei= true error

Xi = measured valueX = true value of the measured parameter- The true value of a survey measurement is never known and can never be determined exactlyTherefore , true error can never be determined

Ѵi= xi-xᴖ

Where : Ѵi = estimate of the true error ei

xᴖ = estimated true valueXi = measured value

- how close the estimates Ѵi to the true ei

Depends on the closeness of xᴖ to the true value X

error types :1. blunders2. Systematic errors3. Constant errors4. Random errors

Blunders errors:Definitions: personal mistakesCause: human carelessness, fatigue and hastDetection: huge value of error Vi > 3σ

Correction: delete the measurement

Systematic errors:Definitions: Errors associated with mathematical formulaCause: some maladjustment of the surveying instruments, personal bias and the natural environment such as temperature (expansion or contraction)Detection: environmental phenomenonCorrection: modeling ( mathematical expression)

Example : the change in length of steel measuring tape due to change in tempSystematic errors can be any sign (- or +)

Random errors:Definitions: Small value error associated with random lessCause:Human nature and instrument capabilityDetection:Vi < 3σ ( its follows the normal distribution)Correction:Repeat measurement , use better instrument Example:Reading tape measurements several times (trial)

Characteristic of random errors: positive and negative errors of the same

magnitude occur with equal frequencySmall errors occur more frequently than large

onesVery large error seldom occurIf we have a specific distance measured

100000 times. The mean is computed, and the estimated error in each measurement is computed by abstracting the mean vale from the measured value( called deviation from the mean)

The curve is symmetrical about v=0

Normal (Gaussian ) distribution:

Normal distribution:

Probability of random error

Normal distribution:

Example 1: a measured distance has a standard error of + 0.05 m - there is 68.3 % probability that the random error in the measured value falls within the range + 0.05 m (1σ)-there is 95.4 % probability that the random error in the measured value falls within the range + 0.1 m (2σ)-there is 99.7% probability that the random error in the measured value falls within the range + 0.15 m (3σ)

- The standard error of a measurement can be determined if the exact distribution pattern of the random error is known. This means the measurements should be repeated infinite number of times

- In practice , number of measurements is limited (< 10 times), therefore, only an estimated value of the standard error can be computed

Mean, Standard Deviation, and Standard error of the Mean

Standard error of the mean

Example 2:-A distance was measured ten times yielding the following results:574.536 , 574.533 , 574.530 , 574.531 , 574.532 , 574.534 , 574.535 , 574.531 , 574.531 , 574.533 , Compute:The meanStandard deviation Estimated standard error of the mean

Probable error and maximum errorProbable error of a measurement = 0.6745σ-i.e their is 50% probability that the actual error exceeds the probable error, as well as 50% probability that is less than the probable errorExample-3:If the standard error of an angle is + 1.5 sec, the probable error of the angle = + 0.67458*1.5 = +1.0 sec

maximum error of a measurement i.e there is 99.7% probability that the actual error falls within 3σ , and there is only 0.3% probability the actual error exceeds 3σ

Example 4:If the standard error of a distance measured is + 0.05 ft, then the maximum error = + 3*0.05ft = + 0.15ft

Precision and accuracy:Precision: how far the measurements are

from each other (for repeated measurements)Accuracy:How far the measurements are from the true

valueIf σ is low then precision is highIf σ is high then precision is low

Example: measurement “A” with standard deviation + 0.05 m and measurement “B” with standard deviation +0.10Measurement “A” more precise than measurement “B”High accuracy close to the true value

High accuracy, but low precision high precession, but low accuracy

Repeated measurements

Law of propagation of random errors

Law of Propagation of random errors relates the estimated standard error of computed parameter to the estimated standard error of the measured parameters

Error of sum:

Example:A line is measured in three sections as follows:L1= 753.81+0.012L2=1238.4+0.028L3=1062.95+0.02Determine the lines total length and its anticipated standard error

Solution:Total length= L1+L2+L3 = 753.81+1238.4+1062.95 = 3055.16

=+ 0.036ft

Principles of least square- The method of least square is based on:1.There are more measurements than the min

number needed to determine the unknown parameters

2.The measurements contain only random error3.The measurements are made independently

from each other

Let X1, x2, ……, xn be the measured value of n parametersAnd v1, v2, ……, vn be the error in theses measured valuesAnd σi be the standard error of the measurement Xi then the most probable solution to the unknown survey parameters is that which satisfies the following condition:

where σo = constant

Weight and weighted mean 

wwwxwxwxwx

n

...........

........

21

222211^

n

ii

x

w

^

Example-9Given the following independent measurement

Compute the weighted mean and an estimate of the standard error of the weighted mean

ft

ft

ft

xxx

7.151

3.151

4.151

3

2

1

ft

ft

ft

3.0

1.0

2.0

^

3

^

2

^

1

Solution:assume ft3.0

3

1

3

00.9

2

25.2

1

3.03.0

1.03.0

2.03.0

22

3

22

2

22

1

w

w

w

Cont…..

wwwxwxwxwx

n

...........

........

21

222211^

ftx

x

35.151

1925.2

7.15113.15194.15125.2

^

^

Cont……

ftx

09.025.12

3.0^

n

ii

x

w

^

Significant figuresThe significant figures in a number are those

digits with known values. They are identified by proceeding from left to right beginning with non zero digits and ending with the last digits of the number

All non zero digits are significant Zeros at the beginning of the number are not

significantZeros between digits are significantZeros at the end of a decimal number are

significant

Example 10541.6800

7 significant figures50.0006

6 significant figures

0.00058 2 significant figures

0.006200 4 significant figures

8.0000507 significant figures

51.0 3 significant figures

Example 11:72300 3 0r 4 or 5 significant figure

It can be written as :72.3*10^3 3 S.F72.30*10^3 4 S.F72.300*10^3 5 S.F

Rounding off- If the result is to be expressed to n significant figure , the nth figure should be retained as is if the (n+1)nt

place < 5 - The nth sholud be increased by one unit if the (n+1)nt

Figure is >5- If the (n+1) digit is 5, round off to the nearest even digit in the nth place

Example 12:6756.589 round off to 5 significant places

6746.6468.767 round off to 5 significant places

468.77468.762 round off to 5 significant places

568.76458.755 round off to 5 significant places

468.76468.745 round off to 5 significant places

468.74

Example 1372.32 4.S.F 3.S.F 72.3

72.37 3.S.F 72.4

72.35 3.S.F 72.4 Odd case

72.45 3.S.F 72.4 Even case

Rounding offWhen performing addition of or subtraction

the sum cannot be more precise than the least precise number included in the addition

Example -14 24.217 468.46 1,553.1 2,055.777 ftThe sum should be expressed as 2,055.8 (one

digit after the decimal)

Unit of measurementUnit of measurement used in US are:Length:1 foot = 12 inches1 yard = 3 feet1 meter = 39.37 inches = 3.2808 feet1 Rod = 16.5 feet1 Gunter's chain = 66 feet = 4 rods1 mile = 5280 feet= 80 Gunter's chains Area:Acre= 10 square chains = 43, 560 ft2Hectare = 10,000 m2 = 2.471 acres

Unit of measurement used in SI system :Length:1 meter = 1,000,000 micrometer1 meter = 1,000 millimeters1 meter = 100 centimeters 1 kilometer(km) = 1,000 meters

Area :Acre = 43,560 ft2Hectare = 10, 000 m2 = 2.471 acres

Conversion of length unit

1 US yard = 0.91441 meter = 39.37 inches1 foot = 0.3048 meter1 inches = 25.4 millimeters

Method of Measuring Distances1. Pacing:a) for short distances < 100mb) Accuracy 1/50 to 1/100

2. Stadiaa) Horizontal distance is measured through

measuring the vertical angle and elevation differences (will be discussed later)

hAB

3. odometer:Measured distance = no of rounds

4. speedometer:Approximate

5. Knowing the time:By knowing the travel time and velocity then the distance can be found as :

r2

tVL .

6. Electronic distance measuring (EDM) equipment:- use electromagnetic waves to measure distances with high accuracy (will be discussed later)

7. chain:-Set of chains connected together with 10, 20 or 25 meter in length8. tapes:

Tapes:1. Steel tapes2. nickel tape 3. Woven tapes

Tapes:Type of tape:1.Woven tape2.Steel tape

Tapping accessories1. Range poles: to clear the line of tapping2. Chaining pins(arrow): to mark tape ends ends on the ground3. Tension handle: used to apply appropriate pull to the tape4. Thermometer 5. Plumb bob: the position of the end of the

tape is transferred to the ground

Range poles: chaining pins

1. Tension clamp:No never tension neither sag

2. Thermometer to find out the expansion

Measuring Distances 1. Horizontal distances2. Vertical distances3. Slope distances

Horizontal distances most common used

Measuring horizontal distances1. Direct measurement2. Indirect measurement a) horizontal distance calculated from the

slope distance “s” and the vertical angle “α” then the horizontal “L” distance will be:

cosSL

b) Horizontal distance calculated from the slope distance “S” and the difference in elevation between the beginning and the end of the sloped distance

hS

hSLhLS

L22

222

222

c) Horizontal distance calculated from the difference in elevation between the beginning and the end of the sloped distance “h” and the vertical angle “α”

tan

tan

hL

Lh

Measuring distancesa) Short distance at flat terrain (d<L)b) Long distance at the flat terrain (d>L)c) Short distance at slope terraind) Long distance at slope terrain

Tape length = LMeasured distance = d

Measuring distancea) Short distance at flat terrain d<LRanging to keep the same line

b) Long distance at flat terrain

D>LUse 3 poles at straight line ranging. Put chaining pins

2.852.25230

Long distance at flat terrain

c) Short distance at slope terrain

d<LRanging + plumb bob

Long distance at slope terrain d>L ranging + plumb bob

dddd AB 321

Long Distance at Slope Terrain

Chain surveying- It is based on measuring the longitudinal

distances in addition to some other tools to establish offset direction (perpendicular lines)

- It is used in surveying small area (few acres)- It is used in open areas no obstaclesTools used in chain (tape) surveying:1.Tapes and its accessories 2.Double right angle prism3.Cross staff

Double right angle prism:-To establish the offset direction -Consist of two right angle prisms, a piece of viewing glass, and alight weight plummetThe upper prism provides a view to the rightThe lower prism provides a view to the leftThe view in the front of the prism is seen through the flat viewing glass mounted between the two right angle prism

double right angle prism

Ranging out survey lines:1.Direct ranging by eye a) forward ranging

Ranging out survey lines:b) Backward ranging

Ranging out survey lines2. Indirect or Reciprocal Ranging used when the two fixed points A and B can not be seen from each other

3. Ranging out in valleys and steep slops Fix two ranging poles out side the steep area then use another pole with plumb bob fixed to it with a line ( about 1.5 m long)

3. Ranging out in valleys and steep slops

Setting out right angle1. Double right angle prisim

2. Cross staff

4. Pythagorean theory

3. Pythagorean theory

Drawing arcs:

5. Drawing half circle

Taking offset1. Double right angle prisim

2. Cross staff

3. Draw arc: to take offset from point D (out side line AB) to the line AB:

4. The shortest line from a point to the line AB is the

Establish a line parallel to the base line and pass in a point 1. Base line AB, to draw a line parallel to AB

and passes through a point such as M

2. Base line is AB, to draw a line parallel to AB and passes through a point such as M:

Establish a line parallel to the base line pass in a point

3. Base line AB, to draw a line parallel to AB and passes through a point such as M :

N M

C EA B

D

4. Base line AB, to draw a line parallel to AB and passes through a point such as M:

Overcome obstacles 1. obstcals obstructing chaining but not (vision ) ranging:-Measure the distance between points A and B, given that both points can be seen from each other of them can not be reached -Case 1:-Make perpendicular line from point B to point C-From another point B to point D make another perpendicular to point E on the line of AC

Cont… 1. obstacles obstructing chaining but not (vision ) ranging case 1:

Cont…. 1. obstacles obstructing chaining but not (vision ) ranging case 2:Choose a point on AB say D then make perpendicular from point D to point DDivide DE at middle say at point NFrom point E make perpendicular line on point C given that C on line AN (same extension)From another point on AB say point D make another perpendicular to point E on the line of AC

Case 2 cont….Note : the symmetery between the two

triangles AND & NCE, then AD = ECAB = AD + DBAB = EC + DB

1. obstacles obstructing chaining but not (vision ) ranging , two points separated by an obstaclesCase 1: From point B mke perpendicular line to point DFrom point A make perpendicular line to point C that BD=AC

1. obstacles obstructing chaining but not (vision ) ranging , two points separated by an obstaclesCase 1:

correctionsLength correction

-Length correction : the difference between the nominal length of a tape and the actual length under the conditions of calibration-E.g if nominal length of a tape is 100 ft but actual length after calibration was found to be = 100.02 ft this tape is too long (add the differences to be measured between two fixed points)-E.g if nominal length of a tape is 100ft but actual length after calibration was found to be 99.98 ft this tape is too short ( substract the difference on distances to be measured between two fixed points)

L

l

llC l '

'

Example 15:The nominal tape length is 100 ft and actual length is 100.02 fr, a distance is measured using this tape found to be 705.56ft, what is the corrected length for this measurement?Sol:

9.70514.076.705

14.0

76.706100

10002.100'

'

CLC

llC

lcorr

l

l

L

ft

Ll

Temperature correctionTemperature correction: to correct the observed length of a survey line because of the effect of temperature on the steel

Where:0.00000645 is the coefficient of thermal expansion of steel per 1 F0.0000116 is the coefficient of thermal expansion of steel per 1 CT1: field tempTo: temp under which the tape is calibrated L: the length of the line

L

L

TTCTTC

t

t

)(0000116.0

)(00000645.0

01

01

Example 16:- A distance was measured to be 500 ft at 83⁰

F, the tape was calibrated at tempreture of 86⁰ F , find the corrected length of the distance:

Corrected length = 500+0.048 = 500.048ft

ft

L

CC

TTC

t

t

t

048.0

500)8683(00000645.0

)(00000645.001

Sag correctionSag correction: the difference between the axial length of the tape hanging in the space and the chord distance between the ends

-where:W:the total weight of the section of the tape between supports w: weight per foot of the tapeP: the tension on the tapeL:the interval between supportsUnits should be compatible for weight and tension (i.e lb or kg)

PWC

Ls 2

2

24

PLwC s 2

32

24

Example 17:- A 100 ft steel tape weight 2 lb and is

supported at the ends only with a pull of 12 lb, find the sag correction

PWC

Ls 2

2

24 ftC s

12.024

100

122

2

2

Example 18:A 30 m steel tape weight 0.336 kg and is

supported at 0, 15 , and 30 m points with a pull of 5 kg, find the sag correction

m001.0224

15

5168.0

2

2

PWC

Ls 2

2

24

Tension correction:Tension correction: the elongation of the tape

of length L in feet

- Where :

Cp: the elongation of the tape of length L in feet

P1: applied tension in lb

P0: the calibration tension in lb

A: cross sectional area of the tape in in2

E: the modulus of elasticity of the tape material(for steel 29,000,000 psi)

AE

LPPC p01

_

Example19- A 100 ft steel tape having a cross sectional

area of 0.0046 in2 , is correct length under a pull of 12 lb, calculate the elongation (nearest 0.001 ft)due to a tension of 20 lb)

AE

LPPC p01

_

ft0046.0

)000,000,29)(0046.0(

1001220

Slope correction:

hsd22

Where: s: slope correction h: vertical distance d: horizontal distance

Chh

dsh

sdsds

dsds

2

2

222

))((

C

hC

g

s

sds

2

2

Where :Cg: slope correctionS: slope distanceh : vertical distance d: horizontal distance

Slope and alignment errorsExample 20:What error results from having one end of the 30 m tape:a)Off line by 0.1 m

b) Too low by 0.8 m

0002.0000167.0

30221.022

shC s

011.00107.0

30228.022

shC s

Accuracy- Under normal field conditions good field procedure, using , and using a good quality tape (calibrated to + 0.02 ft) a standard error 1/3000 can be achieved without applying any corrections -By applying corrections for all known sources of a systematic errors , a standard errors of 15,000 may be achieved:Tape length calibrated with standard error=+0.006ftField tension measured with standard error of + 2 lbField temperature measured with standard error of +5 FSlope determined with standard error of +0.5%Standard error of pin marking <+0.01ft

Basic principle of geomatric tape surveyinga) Basic triangle: measure the three sides of

the triangle to locate the three pointsb) If two points on the triangle are defined the

thired point can be defined using the intersection method

c) If the two points A and B are defined then any other points can be defined by measuring offset distance from the line AB

d) A right triangle can be established by using the proportion 3-4-5 for the three sides

Leveling

DEFINITIONSElevation of a point : is vertical distance above ore below a surface of reference called datumLeveling: the operation of determining the difference in elevation between pointsElevation datum: Datum surface is any level surface to which the elevations of all points may be referred. The mean sea level is usually adopted as datum.Mean sea level(MSL): the average height of the surface of the sea for all stages of the tide at that particular location

Bench marksBench marks are stable reference points the

reduced levels of which are accurately determined by leveling.

o Temporary bench mark:A point with known elevation within the project

itself used as a reference to determine the elevation for other points in the project site

Back sight (BS)This is the first reading taken with a leveling

instrument in a leveling operation.

Foresight (FS)This is the last reading taken in a leveling

operation.

Intermediate Sight (IS)This is the reading taken between the back

sight and foresight in a leveling operation.

• Turning Point (TP)A change point or turning point is a staff

station on which two staff readings are taken without changing the position of the instrument.

Instrument hight (IH)The elevation of the sight line

Staff reading:M= (U+L)\2LevelingRough sightingFocusing Take reading

Reciprocal levelingExample 23Find RLB if you know RLA = 810.167

A1=3.5 , b1 = 2.8A2 = 3.95 , b2= 3.2Solution:

mRL

baba

B

AB

AB

892.810725.0167.810

725.02

)2.395.3()8.25.3(2

)()(2211

How right location for the leveling instrument- The right location for the leveling instrument

is between the two target points at the middle (not necessary on the same line)

- When the level at the middle between the two points (not necessary on the same line ) the error will have no effect

- The right reading on staff A is a1, and on staff B is b1

- There is an error because of the sight line not horizontal (there is angle α)

- The difference in elevation between A and B is

a1 – b1=But a1= a2- L tan αAnd b1= b2-L tan αThen a2-L tan α –(b2- L tan α)= a2-b2a1-b1=a2-b2If the level located between two points at the

middle then the difference in elevation between these two points is the same even if there is an error in the reading due to instrument , weather or earth curvature

Profile LevelingThe process of determining the elevations of a series of points at measured intervals along a line such as the centerline of a proposed ditch or road or the centerline of a natural feature such as a stream bed.

Profile leveling yields elevations at definite points along a reference line.• Used in designing linear facilities:HighwaysRailwaysCanalsSewers

Staking and Stationing the Reference LineTo Stake the proposed RLStaring, ending and angle points will be set first♦ Intermediate stakes will be placed on line (50 to 100 ftEnglish units or 10 to 50 m SI units)♦ Distances for staking will be taped, measured (usingEDM …)

Example of Profile leveling

determine the area of a tract of land bordered by the high water line of a stream, offsets from a transit line were measured at regular intervals of 30 ft as follows: 20.8, 16.7, 21.5, 29.3, 31.0, 25.1, 15.7, 18.0, and 23.2ft. fined the area by using trapezoidal rule in (ft2)