3- Levelling.pdf

Survey Basics (CE 112)

Dr. Waleed Tahawy

Qassim University

Unaizah College of Engineering

Civil Engineering Department

Definitions and Concepts

Dr. Waleed Tahawy


Definitions

• Leveling is the process used to determine a difference in elevation between two points.

• A Level is an instrument with a telescope that can be leveled with a spirit bubble.

• An Elevation is a vertical distance above or below a reference datum.

• Datum is an assumed or a fixed reference plane.

• Mean Sea Level (M.S.L.) is a reference datum for levelling.

Dr. Waleed Tahawy


Definitions

• A vertical Line is a line from the surface of the earth to the earth’s center. Plumb line, line of gravity.

• A level Line is a line in a level surface.

• A Level Surface is a curved surface parallel to the mean surface of the earth.

• A Horizontal Line is a straight line perpendicular to a vertical line.

Dr. Waleed Tahawy


Definitions

• Benchmarks (B .M) Are fixed points information site and attributed placed in different places until you start racing them when conducting settlement.

• Back sight (B.S.) Is the first reading taken after placing the device in any position so that we see the greatest possible number of points required to find the elevation.

• Fore sight (F.S) Is the last reading taken before transfer the device.

Dr. Waleed Tahawy


Definitions

• Benchmark (B .M )

Dr. Waleed Tahawy


Definitions

• Intermediate sight (I.S.) Is reading taken between the back sight and fore sight reading.

• Elevation of line of sight (H.I) Is the imaginary vertical level determined by the line of sight to the amount of increase or decrease for sea level.

Dr. Waleed Tahawy


Equipment

Level Instrument

Dr. Waleed Tahawy


Equipment

• A level is an instrument giving horizontal line of sight and magnifying the reading at a far away distance.

• It consists of the following parts:

(i) A telescope to provide a line of sight

(ii) A level tube to make the line of sight horizontal and

(iii) A leveling head to level the instrument

Dr. Waleed Tahawy


Equipment

• The level parts

Dr. Waleed Tahawy


Equipment

• Automated Levels - Easy to use (not power!)

- Needs experience

- Robust even in hostile environment

• Digital Levels - Push-button technique

- No reading errors, special staff

- Readings are stored and analyzed digitally

Dr. Waleed Tahawy


Equipment

• Tripod is a portable three-legged frame, used as a platform for supporting the weight and maintaining the stability of some other object

Tripod plumb bob

Dr. Waleed Tahawy


Equipment

• Staff Is a wooden or metal ruler one side runway to meters and centimeters. And is a ruler of solid wood 2 , 3 , 4 , 5 meters in length and usually 4 meters.

• INVAR type for high

precision leveling

Dr. Waleed Tahawy


Equipment

• Staff

Conventional (“E”-type) Barcode

for Digital Levels

Dr. Waleed Tahawy


Equipment

• Pole staff bubble (bull eye)

• Keep the pole upright

– Any tilt will disturb your readings

Dr. Waleed Tahawy


Equipment

• Survey Markers

• Gives you a fixed point

– Should be of good quality

– Should be long-term

– Preferable in bedrock, settled buildings, or bridges

– Do not use fences or walls

Dr. Waleed Tahawy


Equipment

• Survey Markers

Dr. Waleed Tahawy


why?

• Why do we perform leveling surveys?

• To determine the topography of sites for design projects

• Set grades and elevations for construction projects

• Compute volumes of earthwork

Dr. Waleed Tahawy


Method of measuring

• A Level is an instrument with a telescope that can be leveled with a spirit bubble. The optical line of sight forms a horizontal plane, which is at the same elevation as the telescope crosshair. By reading a graduated rod held vertically on a point of known elevation (Bench Mark) a difference in elevation can be measured and a height of instrument (H.I.) calculated by adding the rod reading to the elevation of the bench mark.

Dr. Waleed Tahawy


Method of measuring

• Once the height of instrument is established, rod readings can be taken on subsequent points and their elevations calculated by simply subtracting the readings from the height of instrument.

Dr. Waleed Tahawy


leveling

• Leveling of the instrument is done to make the vertical axis of the instrument truly vertical. It is achieved by carrying out the following steps:

• Step 1: The level tube is brought parallel to any two of the foot screws, by rotating the upper part of the instrument.

• Step 2: The bubble is brought to the center of the level tube by rotating both the foot screws either inward or outward. (The bubble moves in the same direction as the left thumb.)

Dr. Waleed Tahawy


leveling

• Step 3: The level tube is then brought over the third foot screw again by rotating the upper part of the instrument.

• Step 4: The bubble is then again brought to the center of the level tube by rotating the third foot screw either inward or outward.

• Step 5: By rotating the upper part of the instrument through 180°, the level tube is brought parallel to first two foot screws in reverse order. The bubble will remain in the center if the instrument is in permanent adjustment.

Dr. Waleed Tahawy


leveling

Dr. Waleed Tahawy


Leveling Principle

• Basic Principle of Leveling

• Measures height differences between points

– Along a line

– Several points from one occupation

Leveling rods

Line of sight

Back sight Fore sight

Gravity Gradient

bs

fs

Dh = bs - fs

Dr. Waleed Tahawy


Taking readings • Method of taking readings on a ruler settlement

• direct leveling a back sight is taken on the rod held at the bench mark ( A ) .

H..I = E.L.V of B.M. ( A ) + B.S.

• Turning the telescope to bring

into view the rod held on point B

afore sight is taken .

• elev. Point B = H .I – F .S

• check the work by the following equation:

• ∑ B.S. - ∑ F.S. = Last R.L. – First R.L.

1422

Dr. Waleed Tahawy


Basic Rules for Leveling

• Always start and finish a leveling run on a Benchmark (B.M.) and close the loops.

• Keep fore sight and back sight 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

• Beware of shadowing effects and crossing waters

Dr. Waleed Tahawy


Leveling Errors & Mistakes

• Curvature & Refraction

• Curvature Error is the divergence between a level line and a horizontal line over a specified distance.

Level

Horizontal

Ver

tica

l d

c

Dr. Waleed Tahawy




• Refraction Error is the caused by earth’s atmosphere. It is about 1/7 of the curvature error.

Dr. Waleed Tahawy



• Effects of Curvature & Refraction Errors

Level

Horizontal

Ve

rtic

al

d E

O

A

Line of Sight

B c

r

c + r

AB = r

AE = c

BE = c + r

R

K

Dr. Waleed Tahawy




• Computation of Curvature Error

mAKkmAKAK

c

kmR

R

AK

cR

AKc

222

22

0785.00000785.063702

6370

22

Dr. Waleed Tahawy



• Combined Curvature & Refraction Error

• Refraction is affected by:

• Atmospheric Pressure, Temperature and Geographic Location

r = 1/7 c = 0.14 c

(c + r) m = 0.0675 K2

K = KA, the length of sight in km

Dr. Waleed Tahawy



• Combined Curvature & Refraction Error

• Selected Values for (c + r) and Distance

Distance (m)

30 60 100 120 150 300 1000

(c + r)m

0.0001 0.0002 0.0007 0.001 0.002 0.006 0.068

Dr. Waleed Tahawy



• Example • Compute the error due to curvature and refraction for the

following distances:

a) 400 m b) 3,000 m c) 4 kilometers

• Solution:

c + r = 0.0675 K2

- Where, K, is the length of sight in kilometers and (c + r) in meters.

a) (c + r) = 0.0675 (0.4)2 = 0.0108 m

b) (c + r) = 0.0675 (3)2 = 0.6075 m

c) (c + r) = 0.0675 (4)2 = 1.080 m

Dr. Waleed Tahawy



• Parallax Error: is an error in sighting that occurs when

the objective and/or the cross hairs are improperly

focused.

• When the surveyor observes apparent movement of the

cross hairs on the rod (parallax), he should carefully

check the cross-hair focus adjustment and the objective

focus adjustment for consistent results.

Dr. Waleed Tahawy



• Level Loop Adjustments

• level surveys have to be closed within acceptable

tolerances or the survey would have to be repeated. The

tolerances for various orders of surveys were shown in

Table

• If a level survey were performed to establish new BMs, it

would be desirable to proportion any acceptable error

throughout the length of the survey. Because the error

tolerances shown in table are based on the distances

surveyed, adjustments to the level loop are based on the

relevant distances, or on the number of instrument setups,

which is a factor directly related to the distance surveyed.

Dr. Waleed Tahawy



• Precision (Vertical Control Networks)

Order of Precision

Maximum Closures (mm)

First - Order

Second - Order

Third - Order

Fourth - Order

K3

K5

K12

K25

Dr. Waleed Tahawy



• Problem

• A closed loop of differential levelling was run to establish

the elevations of points P2, P3, P4 and P5. P1 has a known

elevation 643.44 m above M.S. L. If, the elevations of

points P1, P2, P3, P4 and P5 are computed from the

observed measurements and shown in the Table below

along with their distances from P1. Compute the adjusted

elevations of points P2, P3, P4 and P5.

Dr. Waleed Tahawy



• Solution

• Total error (correction) e = HP1 (fixed) – HP1 (computed)

• e = 643.44 – 643.93 = - 0.49 m

P2

P1 P3

P4 P5 5 km

Dr. Waleed Tahawy



• Solution • The allowable error for a second-order, class II survey is

; thus, = 0.025 m is the permissible error.

Points

Distance from P1 (km)

Com. Elev. (m) Correction (m)

Adjusted Elev. (m)

P1 0 643.44 - 643.44

P2 7 657.34 - 0.14 657.20

P3 13 645.68 - 0.26 645.42

P4 16.5 630.06 - 0.33 629.73

P5 21.5 641.11 - 0.43 640.68

P1 24.5 643.93 - 0.49 643.44

K5

5.24005.0

Dr. Waleed Tahawy


Leveling Errors & Mistakes • Solution • Correction for each elevation = e cumulative distance/ total

distance

• Correction for HP2 = - 0.49 7/24.5 = - 0.14 m

• Correction for HP5 = - 0.49 21.5/24.5 = - 0.43 m

• Correction for HP1 = - 0.49 24.5/24.5 = - 0.49 m

• Compute the adjusted elevations of points P2, P3, P4, P5 and

P1 as follows:

• HP2 = 657.34 + (- 0.14) = 657.20 m

• HP3 = …………

• HP4 = …………

• HP5 = 641.11 + (- 0.43) = 640.68 m

• HP1 = 643.44 + (- 0.49) = 643.44 m

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3- Levelling.pdf