chapter 5 edited

8/2/2019 Chapter 5 Edited

1/56

Chapter FiveLevelling

Bahir Dar UniversitySchool of Civil and Water Resource

Engineering


2/56

Definition

It is the art of measuring relative altitudes of points on the

surface of the earth of beneath the surface of the earth.

It involves the measurement of vertical distance relative to

a horizontal line of sight.

Definition of basic termsDatum:- A datum is any reference surface to which the

elevation (vertical distance) of a points are referred.

Elevation: - Elevation is the vertical distance of a pointsabove or below on assumed datum (level surface).

Leveling:- The process or methods of determining thevertical distance of a points relative to on assumed

level surface.


3/56

Cont...Level line:- is the surface of which it has a constant height

relative to mean sea level.

Horizontal line:- this is a line which is tangential to thelevel line or a line which is normal to direction of gravitas

Bench Mark (BM):- are permanent reference points or

marks at which their elevation (reduced level) has beenaccurately determined by leveling from other permanentBM.

Reduced level (RL):- is the height above or below a

reference datum- similar to elevation.Temporary bench mark (TBM):- are marks let up on

stable points near construction sites which all leveling

operation on that particular site will be referred.

Mean sea level(MSL) : - it is the average observation of


4/56

Cont...Back sight (BS):- is the staff reading taken on points of

known elevation as a BM or a turning points.

Fore Sights (FS):- is the staff reading on points whoseelevation is to be determined as a turning points. It is thelast staff reading denoting the shifting of the instruments.

Intermediate sights (IS):- any other staff reading taken on

a points at unknown elevation from the same set up ofthe level. All sights b/n BS & FS are IS.

Turning points (TP):- is a point denoting the shifting at thelevel. It is the point on which the back a fore sight are

taken.Station:- is a points of which whose elevation is to be

determined.

Instrument station : - the point where the instrument is set

up for observation.-


5/56

Cont...


6/56

Equipments used in leveling

Level to give the true horizontal line

Staff to read vertical heightTape to measure height of instruments

Note: There are three types of level

TiltingAutomatic

Digital


7/56

Classification of levelling

1. Simple levelling

2. Differential levelling

1. Simple levelling : -type of operation fordetermining the difference in elevation between

two points visible from a single point of the level.(reading by one set up)

Note : - in order to eliminate the effect of earthcurvature and instrumental error it is always

advisable to set up level on approximate equallength.

2. Differential levelling : -the method of determiningthe difference in elevation of two points wither too

far apart or obstructed by an intervening ground.


8/56

Principle of leveling

The instruments are set up and correctly leveling in order

to make the line of sight through the telescope horizontal.

With the instruments set up approximately midway betweenground points A & B. If the reduced level (RL) of points Ais known and equals to 100,000m above a certainreference datum then the reading at 3.00m on vertically

herd staff at A gives the reduced level of horizontal line of


9/56

Cont...

This sights on to A is termed as back sights (BS) and

reduced level of the line of sights is called height of planeat collimations (HPC)

Thus, RLA + BS = HPC . . .

The reading of 1,000m on to staff a B is called foresight (FS) and shows the

ground point B to be 1,000 below HPC therefore its RL = (103,0001,000)=102.000

Then this is the basic concept of leveling which is then developed in to followingleveling.


10/56

Cont...

Let RL be reduced level

R = Staff reading.Then

RLC = TBM

RLD = RLC + (RC

RD)RLE = RLC + (RC RE)

RLF = RLE + (RE RF)

RLG = RLE + (RE RG)


11/56

Method of bookingThere are two methods of booking in the field for leveling.

I. Rise & fall method

II. Height of collimation method.Method 1-Rise & fall method

The basic concept of rise and fall is illustrated as shown below.(Refer the fig above)

Let RLC = TRM = 100, 000m above BMThe line of sight from the instruments at A is truly horizontal. Itcan be seen that the higher reading of D i.e 2.50 indicatesthat it is lower than C (TBM).

This can be written

1.5 2.50 = -1.0 indicated fall from C to D

Similarly from C to E

1.5 0.5 = +1.0 indicating the rise from C to E.

If the reduced level of TBM = RLC then

RLD = RLC + (RC RD) but RC RD = fall


12/56

Cont...RL D = RL C + fall

RLE = RLC + (RC RE)But RC RE = Rise

= 100 + 1 = 101

RLE = RLC + rise.

CHECKS : -

Staff

Position

BS

(m)

IS

(m)

FS

(m)

Rise

(m)

Fall

(m)

RL

(m)

Remark

C 1.5 100.0 TBM

D 2.5 1.0 99.0

E 2.0 o.5 2.0 101.0 TP

F 2.5 0.5 100.5

G 3.0 0.5 100.0

FirstRLLastRLFallRiseFSBS


13/56


14/56


15/56

The comparison of line of collimation methodand Rise fall method


16/56

Longitudinal and X-sectional levelling

Longitudinal levelling : -This type of levelling is used to

produce ground profiles for use in the design of roads,railways and pipelines.

In the case of such projects, the route centre-line is set out

using pegs at 10-m, 20-m or 30-m intervals. Levels are

then taken at these peg positions and at critical points suchas sudden changes in the ground profiles, road crossings,

ditches, bridges, culverts, etc. The resultant plot of these

elevations is called a longitudinal section. When plotting,

the vertical scale is exaggerated compared

with the horizontal.


17/56

The longitudinal section is then used in the vertical

design process to produce formation levels for theproposed route design.

It gives information along a centre-line only

Cont...


18/56

Cross sectional Levelling : -

It gives information at 90 to the centre-line for

2030 m on each side of the selected work.


19/56

Misclosure, Limits and its distribution

Misclosure is leveling operation are an indication of theaccuracy of the work. It is important to realize the

amounts of misclosure in leveling can only be assessedby

Connecting the leveling back to the BM from which it

started or

Connecting in to another BM of known and groundelevation

When the misclosure is assessed, one must then decide if it isacceptable or not

Alternating the permissible may be based on the distancetraveled or no. of set up involved

A Common Criteria used to assess the misclosure (E) is

E =

KM


20/56

Cont...

In many case in Engineering the distance involved is quite

short but the no. of setup is quite high, in which case thefollowing criteria most be used .

E=

Where n = No ob instrument setup

M = Constant is mm ( 5)

If the misclosure is outside the allowable then the levelingmust be repeated and if it is with in the misclosure has tobe contributed equally to all set up

Correction per set up =

nM

n

E

L i di l d X i l l lli


21/56

Longitudinal and X-sectional levelling

Longitudinal levelling : -This type of levelling is used to

produce ground profiles for use in the design of roads,railways and pipelines.

In the case of such projects, the route centre-line is set out

using pegs at 10-m, 20-m or 30-m intervals. Levels are

then taken at these peg positions and at critical points suchas sudden changes in the ground profiles, road crossings,

ditches, bridges, culverts, etc. The resultant plot of these

elevations is called a longitudinal section. When plotting,

the vertical scale is exaggerated compared

with the horizontal.


22/56

Mistakes & errors in Leveling

Some of the mistakes commonly made in leveling are

confusion of the of numbers is reaching of the staff example2.345 2.0 3.345

Recording the back sight is foresight column and vice- versa.

Faulty addition a subtraction of back sight of foresight is

checking every page between bench marks. Rods or staff not held in the same point for foresight and back

sight in turning point. etc.

Instrumental level.

The errors in leveling might occur due to1. Instrumental error

2. Field error.

3. Effect of curvature refraction.


23/56

1. Instrument error: - these are error which occurs due to

the defects of instrument such as.Collimation error-: The error occurs if the line of the

sight is not truly horizontal when the tubular bubble iscentered i.e the line of sight is inclined up or down from the

horizontal.


24/56

Cont...Two peg test: - On relative flat site establish tow pegs A

& B about 50m apart and set up the instruments of P.

H AB = (a1 d1e) (b1 d2e)

Since the instrument is mid way between A & B

d1 = d2

H AB = a1 b1 .. 1

Cont


25/56

Cont...

To check this again set up the leveling at Q of a distance ofd3 (25m) form A or B.

H AB = [a2 (d1 + d2 + d3).e] [b2 (d3.e)]

= (a2

b2)

(d1 + d2).e.. 2

C


26/56

Cont...Equating the two equation

(a1 b1) = (a2 b2) (d1 + d2).e

Therefore collimation error

for filling level an average precision i.e collimation error shouldbe less than 0.00005 red (0.5mm per 10m).

If the error is greater than this the level should be adjusted withthe instruments still set at a horizontal lien of collimation

would give a reading on the staff at A ata1 (d1 + d2 + d3)e

1*2

1122

d

babae


27/56

Cont...

Defect of staff: - It is possible that the staff production

may be incorrect and new or repaired. The staff shall becorrected using steel tape

Tripod defects: - stability of tripod should be checked beforeany field work. If the metal shoes at the base of each leg are

not loose once extended the leg can be tightenedinsufficiently.

2. Field error : - These are errors which occur dueto the following.

1) Staff not vertical2) Handling the instruments & tripod

Cont


28/56

Cont...

3. Effect of Curvature & Refractions (ReadingAssignment)

Cc = 0.0785 D2 , correction for curvatureCr = 0.0112 D2 , correction for refraction

CC= 0.0673 D2 , Correction for curvature and refraction

Assuming the raduis of the arth as 6370Km

Where D is the distance in KmCc combined effect of curvature and refraction in meters

Reciprocal leveling

By means of reciprocal leveling, the need for applying the above

correction may be avoidedreciprocal leveling must be used to obtain accuracy and to

eliminate the following

Error in instrument adjustment

Combined effect of earths curvature and refraction of

atmosphere

C


29/56

Cont...

It is applied when it is not possible to set up the level mid

way between two points as in the case of levelling acrosslarge bodies.

Cont


30/56

Cont...

Taking the average of the two true difference in elevation

i.E Average of two eqns

2 HAB= [a1 (b1 e) + (a2 e) b2]

HAB = [a1-b1] + [a2-b2]

The true difference in elevations, therefore equal to the

mean of two apparent differences is elevations obtainedby reciprocal observation.

Inverted staff readingReduced levels of underside of structures (bridge softest)are determined by using staff in an inverted position ,the inverted staff reading is booked in a relevant column

of the level book with negative sign

*2

1

C t


31/56

Cont...

RLA = TBMHPC = RLA + RARLB = HPC (-RB)

= HPC + RB

Fl l li


32/56

Fly levelingThe permanent bench mark can be located far away from

starting points of proposed road. So, fly leveling should

be done to connect the BM with starting points of thework in order to locates its RL and then calculate RLs of

different points along the alignments.

Note: In fly leveling only the back sight and foresight

reading should be recorded.

T i t i L li


33/56

Trigonometric Leveling

is a process of determining the differences of elevationsof stations from observed vertical angles and knowndistances.

The vertical angle may be measured by means of anaccurate thodolite and the horizontal distances may be

measured in the case of plane or geodetic surveying.

In order to get the difference in elevation between theinstrument station and the object under observation, weshall consider the following cases:

Case 1: Base of the object accessibleCase 2: Base of the object inaccessible: instrument

stations in the same vertical plane as the elevated

object

Case 3: Base of the object inaccessible: instrument

C 1 B f th bj t ibl


34/56

Case 1 Base of the object accessible

R. L. of Q = R. L. of B. M. + S + D tan

Where: - S = reading of staff kept at B. M. with line ofsight horizontal

= angle of elevation from A to Q

D = horizontal distance between P and Q

inaccessible: the instrument stations


35/56

inaccessible: the instrument stations

in the same vertical plane as the

elevated objectCase 2 A: Instrument axis at the same level

R.L. of Q = R. L. of B.M. + S + h

Case B Instrument axis at different level


36/56

Case B: Instrument axis at different level

Example

Case C: Instrument axes at very different level

Case 3 Base of the object inaccessible:


37/56

Case 3 Base of the object inaccessible:

the instrument stations not in the same

vertical plane as the elevated objectExa


38/56

Cont...


39/56


40/56

Cont...


41/56

Cont...


42/56

Cont...


43/56


44/56


45/56


46/56


47/56


48/56


49/56


50/56


51/56


52/56


53/56


54/56


55/56


56/56

chapter 5 edited

Documents