Levelling in Surveying

This slide discusses on introduction to levelling in surveying and types of methods in levelling

1. Royal University of Bhutan
Jigme Namgyel Engineering College
Department of Civil Engineering & Surveying
Tutor : Phurba Tamang
Designation: Associate lecturer
Department of Civil Engineering and Surveying
“ Levelling”
MODULE: SURVEYING
Spring Semester 2020

2. MID-TERM REVIEW, 2017
UNIT 3: LEVELLING
ObjectiveofLevelling:
Theaimoflevellingistodeterminetherelativeheightsofdifferentobjectsonorbelow
thesurfaceoftheearthandtodeterminetheundulationofthegroundsurface.
Uses:
Levellingisdoneforthefollowingpurpose
•Toprepareacontourmapforfixingsitesforreservoirs,dams,barrages,etc.,andtofix
thealignmentofroads,railways,irrigationcanals,etc.
•Todeterminethealtitudesofdifferentimportantpointsonahillortoknowthe
reducedlevelsofdifferentpointsonorbelowthesurfaceoftheearth.
•Topreparealongitudinalsectionandcrosssectionsofaproject(roads,railways,
irrigationcanals,etc.)inordertodeterminethevolumeofearthwork.
•Topreparealayoutmapforwatersupply,sanitaryordrainageschemes.

3. MID-TERM REVIEW, 2017
DEFINITIONS
1.Levelling:Theartofdeterminingtherelativeheightsofdifferentpointsonorbelow
thesurfaceoftheearthisknownasleveling.Thus,levellingdealswithmeasurementin
theverticalplane.
2.LevelSurface:Anysurfaceparalleltothemeanspheroidalsurfaceoftheearthissaid
tobealevelsurface.Suchasurfaceisobviouslycurved.
3.LevelLine:Alinelyingonalevelsurfaceiscalledalevelline.Thislineisnormal
totheplumblineatallpoints.
4.HorizontalPlane:Anyplanetangentialtothelevelsurfaceatanypointisknownas
thehorizontalplane.Itisperpendiculartotheplumblinewhichindicatethedirection
ofgravity.
5.Horizontalline:Anylinelyingonthehorizontalplaneissaidtobehorizontalline.
6.Verticalline:Thedirectionindicatedbytheplumbline(thedirectionofgravity)is
knownasverticalline.

4. MID-TERM REVIEW, 2017
DEFINITIONS
7.DatumSurfaceorLine:Thisisanimaginarylevelsurfaceorlevellinefromwhichthe
verticaldistancesofdifferentpoints(aboveorbelowthisline)aremeasured.The
datumadoptedforthesurveyistheMeanSeaLevel(MSL).MeanSeaLevel(MSL)
adoptedbysurveyofIndiaforreference,islocatedatMumbaiHigh.
8.ReducedLevel(RL)orElevation:Theverticaldistanceofapointaboveorbelowthe
datumlineisknowasthereducedlevelofthatpoint.TheRLofapointmaybe
positiveornegativeaccordingasthepointisaboveorbelowthedatum.
9.VerticalAngle:Verticalangleisananglebetweentwointersectinglinesinavertical
plane.
10.BenchMarks(BM):Thesearefixedpointsormarksofknownelevationwith
referencetothedatumline.Theseareveryimportantmarks.Theyserveasreference
pointsforfindtheRLofnewpointsorforconductinglevellingoperationinprojects.
Benchmarksareof3types:Permanent,ArbitraryandTemporaryBenchmark.

5. MID-TERM REVIEW, 2017
DEFINITIONS
11.BacksightReading(BS):Thisisthefirststaffreadingtakeninanysetupofthe
instrumentafterthelevellinghasbeenperfectlydone.Thisreadingisalwaystakenon
apointofknownRLi.e.onabenchmarkorchangepoint.
12.ForesightReading(FS):Itisastaffreadingtakenonapointwhoseelevationistobe
determined.Itisthelaststaffreadinganddenotestheshiftingofthelevel.
13.IntermediateSightReading(IS):ItisanyotherstaffreadingbetweentheBSandFS
inthesamesetupoftheinstrument.
14.ChangePoint(CP)orturningpoint(TP):Thispointindicatestheshiftingofthe
instrument.BothFSandBSaretakenonthispoint.
15.HeightofInstrument(HI):Whenthelevellinginstrumentisproperlylevelled,theRL
ofthelineofcollimationisknownastheheightofinstrument.Thisisobtainedby
addingtheBSreadingtotheRLoftheBMorCPonwhichthestaffreadingwas
taken.
16.Station:Apointwhoseelevationistobedetermined.Thestaffiskeptatthispoint.

6. MID-TERM REVIEW, 2017
COMPONENTS OF DUMPY LEVEL

7. MID-TERM REVIEW, 2017
COMPONENTS OF DUMPY LEVEL
Tripodstand:Itisaportablethree-leggedframe,usedasaplatformforsupporting
theweightandmaintainingthestabilityofsomeotherobject.
LevelingStaff:Isawoodenor
metalruleronesiderunwayto
metersandcentimeters.Andisa
rulerofsolidwood2,3,4,5
metersinlengthandusually4
meters.

8. MID-TERM REVIEW, 2017
PRINCIPLES OF LEVELLING
Theprincipleoflevellingistoobtainthedifferenceoflevelsoftwopointswiththe
instrumentknownaslevel.Thiscanbeachieveeitherbysimpleordifferentiallevelling.
1.SimpleLevelling:Itisthesimplestlevellingoperationinlevellingwhenitisrequiredto
findthedifferenceinelevationbetweentwopointsbothofwhicharevisiblefroma
singlepositionofthelevel.Thereadingscanbeobtainedonastaffheldsuccessively
uponthepoints.
2.355 m
0.125 m
B.M = 100 m
A B
C
B.S. F.S.

9. MID-TERM REVIEW, 2017
PRINCIPLES OF LEVELLING
Theprincipleoflevellingistoobtainthedifferenceoflevelsoftwopointswiththeinstrumentknownas
level.Thiscanbeachieveeitherbysimpleordifferentiallevelling.
1.SimpleLevelling:Itisthesimplestlevellingoperationinlevellingwhenitisrequiredtofindthe
differenceinelevationbetweentwopointsbothofwhicharevisiblefromasinglepositionofthelevel.
Thereadingscanbeobtainedonastaffheldsuccessivelyuponthepoints.
2.355 m
0.125 m
B.M = 100 m
A B
C
B.S. F.S.
Permanent Benchmark
in Dewathang

10. MID-TERM REVIEW, 2017
PRINCIPLES OF LEVELLING
1.LetAandCbethetwopointsandletthelevelbesetupatBanywhereintheground.Aisa
pointofknownelevationsaybenchmarkofknownR.L.100m.
2.TheinstrumentissetupandlevelledatB
3.ThetelescopeisdirectedtowardsAandthereadingistakenonaverticallyheldstaffatpoint
A.Let,thebacksightobservedatAbe2.335m.
4.ThestaffisthenheldverticallyatpointCwhoseelevationistobefound.Thetelescopeis
directedonthestaffandfocused.BeforesightingthestaffatC,thesurveyorshouldexamine
toseethatthebubblepreservesitscentralposition.Thestaffreadingisthenobtained.Letthe
foresightbe0.125m.
5.ThedifferenceinthetworeadingsiscalculatedandaddedorsubtractedtotheR.L.ofA
dependinguponwhereCishigherorlowerthanA.thedifferenceinthetworeadingsis2.230
m.SinceCishigherthatA,theR.L.ofC=100+2.330=102.230m

11. MID-TERM REVIEW, 2017
PRINCIPLES OF LEVELLING
2.DifferentialLevelling:Determiningthedifferenceinelevationbetweentwoormore
pointswithoutregardtothealignmentofthepointsiscalleddifferentiallevelling.Itis
usedwhen
a.Twopointsareatlargedistance
b.Thedifferenceinelevationbetweenthetwopointsislarge
c.Someobstaclesintervenesbetweenthepoints.
Thismethodisalsoknownascompoundlevellingorcontinuouslevelling.
SupposeitisrequiredtoknowthedifferenceoflevelbetweenAandB.Thelevelissetup
atpointsO1,O2,O3,etc.Aftertemporaryadjustments,staffreadingsaretakenatevery
setup.ThepointsC1,C2andC3areknownaschangepoints.Thenthedifferenceoflevel
betweenAandBisfondout.Ifthedifferenceispositive,AislowerthanB.Ifitisnegative,
AishigherthanB.KnowingtheR.LofA,thatofBcanbecalculated.

12. PRINCIPLES OF LEVELLING
A B
O1
O2
O3
O4
C1
C2
C3
B.S. F.S.
B.S.
B.S.
B.S.
F.S.
F.S.
F.S.
C.P.
C.P.
C.P.

13. MID-TERM REVIEW, 2017
PRINCIPLES OF LEVELLING
3.ProfileorLongitudinalLevelling
Theoperationoftakinglevelsalongthecenterlineofanyalignment(road,railway,etc.)
atregularintervalsisknownaslongitudinallevelling.Inthisoperation,thebacksight,
intermediatesightandforesightreadingsaretakenatregularintervals,ateverysetupof
theinstrument.Thechainagesofthepointsarenotedinthelevelbook.Thisoperationis
undertakeninordertodeterminetheundulationsofthegroundsurfacealongtheprofile
line.
L = Position of Levels C.P = Change Points

14. MID-TERM REVIEW, 2017
PRINCIPLES OF LEVELLING
4.Crosssectionallevelling
Theoperationoftakinglevelstransversetothedirectionoflongitudinallevellingisknown
ascrosssectionallevelling.Thecrosssectionsaretakenatregularintervalssuchas20m,
40m,50m,etc.)alongthealignment.Crosssectionallevellingisdoneinordertoknow
thenatureofthegroundacrossthecentrelineofanyalignment.
L = Position of Levels C.P = Change Points

15. MID-TERM REVIEW, 2017
METHODS OF CALCULATION OF REDUCED LEVEL
Thefollowingarethetwosystemsofcalculatingreducedlevelorelevation
1.Thecollimationsystemorheightofinstrumentsystem(HI)
2.Theriseandfallsystem
1.The Collimation System
Thereducedlevelofthelineofcollimationissaidtobetheheightofinstrument.Inthissystem,the
heightofthelineofcollimationisfoundoutbyaddingthebacksightreadingtotheRLoftheBM
onwhichtheBSistaken.ThentheRLoftheintermediatepointsandthechangepointareobtained
bysubtractingtherespectivestaffreadingsfromtheheightofinstrument(HI).
Thelevelisthenshiftedforthenextsetupandagaintheheightofthelineorcollimationisobtained
byaddingthebacksightreadingtotheRLofthechangepoint(CP).
So,theheightoftheinstrumentisdifferentindifferentsetupsofthelevel.Twoadjacentplanesof
collimationarecorrelatedatthechangepointbyanFSreadingfromonesettingandaBSreading
fromthenextsetting.
Note:
ItshouldberememberedthatinthissystemtheRLsoftheunknownpointsaretobefoundoutby
deductingthestaffreadingsformtheRLoftheheightoftheinstrument.

16. MID-TERM REVIEW, 2017
THE COLLIMATION OR HEIGHT OF INSTRUMENT METHOD
Arithmetical Check:
Thedifferencebetweensumofbacksightsandthatofforesightsmustbeequaltothedifference
betweenthelastRLandthefirstRL.ThischeckverifiesthecalculationoftheRLoftheHIand
thatofthechangepoint.ThereisnocheckontheRLsoftheintermediatepoints.B.S - F.S = Last RL - First RL

17. HEIGHT OF INSTRUMENT
BM D
A
B C
B.S. I.S.
B.S. F.S.
I.S.
C.P.
1.255 1.750 2.150
F.S.
2.750 1.950 1.550
Example:ReferringtothefollowingfigurefindouttheRLoftheunknownpoints.AssumetheRLofthe
benchmarkas100m
EPointstoRemember:
•Stationreferstothepointsofunknownelevation.Commonlyreferstoapositionwherestaffiskept.
•Benchmarkisapointofknownelevation.
•Surveyinghastocommencealwaysfromthebenchmarkwhoseelevationisknown.
•ThereadingtakenontheBMisalwaystakenasBackSight.
•ChangepointsarethepointswhichhasbothForeSightandBackSight.AftertheChangePointthe
positionoflevellinginstrumenthastobechanged.
E

18. HEIGHT OF INSTRUMENT
Station PontBacksight
Intermediate
Sight
Fore SightHeight of Instrument
Reduced Level
or Elevation
Remark
A 1.255 101.255 100 Benchmark
B 1.750 99.505
C 2.750 2.150 101.855 99.105 CP
D 1.950 99.905
E 1.550 100.305
4.005 3.700
•HeightofInstrument=RLofBM+B.SofBM
•RLofnextpoints=HI–Staffreadingofthepoints
•RLofchangepoint=HIfrompreviousinstrumentposition+FSofthechangepoint
•Heightofinstrument=RLofchangepoint+BSofthechangepoint
•SimilarlyRLofnextpoints=HI–Staffreadingsofthepoints4.005BS= 3.700FS= Last RL= 100.305 First RL= 100
0.305 = 0.305

19. MID-TERM REVIEW, 2017
RISE AND FALL METHOD
1.Rise and Fall System
Inthissystemthedifferenceoflevelbetweentwoconsecutivepointsisdeterminedbycomparing
eachforwardstaffreadingwiththestaffreadingattheimmediatelyprecedingpoints.
Iftheforwardstaffreadingissmallerthantheimmediatelyprecedingstaffariseissaidtohave
occurred.TheriseisaddedtotheRLoftheprecedingpointtogettheRLoftheforwardpoint.
Iftheforwardstaffreadingisgreaterthantheimmediatelyprecedingstaffreading,itmeansthere
hasbeenafall.ThefallissubtractedfromtheRLofprecedingpointtogettheRLoftheforward
point.
ArithmeticalChecks:
Inthismethod,thedifferencebetweenthesumofBSsandthatofFSs,thedifferencebetweenthe
sumofrisesandthatoffallsandthedifferencebetweenthelastRLandthefirstRLmustbeequal.B.S - F.S = Rise- Fall Last RL - First RL=   

20. MID-TERM REVIEW, 2017
RISE AND FALL METHOD
Direction of Survey
2.355 m
0.125 m
B.M = 100 m
A
B
C
B.S. F.S. IfStaffReadingatCisless
thanStaffReadingatA,
thereisariseatCinthe
directionofsurvey
2.355 m
0.125 m
B.M = 100 m
C
A
B.S. F.S.
B
IfStaffReadingatCismorethanStaffReadingatA,thereisarise
atCinthedirectionofsurvey
Direction of Survey

21. 2
RISE AND FALL METHOD
BM D
A
B C
B.S. I.S.
B.S. F.S.
I.S.
C.P.
1.255 1.750 2.150
F.S.
2.750 1.950 1.550
Example:ReferringtothefollowingfigurefindouttheRLoftheunknownpoints.AssumetheRLofthe
benchmarkas100m
EPointstoRemember:
•Stationreferstothepointsofunknownelevation.Commonlyreferstoapositionwherestaffiskept.
•Benchmarkisapointofknownelevation.
•Surveyinghastocommencealwaysfromthebenchmarkwhoseelevationisknow.
•ThereadingtakenontheBMisalwaystakenasBackSight.
•ChangepointsarethepointswhichhasbothForeSightandBackSight.AftertheChangePointthe
positionoflevellinginstrumenthastobechanged.
E

22. RISE AND FALL METHOD
•RLofthebenchmarkiswrittenforthestartingpoint.
•DeterminetheRiseorFallofthenextpointandfindtheRLofthenextpointbyaddingorsubtractingtheriseorrun
totheRLofthebenchmark.
•Ifthenextpointisrise,RLisfoundbyaddingtherisefromtheprecedingRL.
•Ifthenextpointisfall,RLisfoundbysubtractingthefallfromtheprecedingRL
Station PontBacksight
Intermediate
Sight
Fore SightRise Fall
Reduced Level or
Elevation
Remark
A 1.255 100 Benchmark
B 1.750 0.495 99.505
C 2.750 2.150 0.400 99.105 CP
D 1.950 0.800 99.905
E 1.550 0.400 100.305B.S - F.S = Rise- Fall Last RL - First RL=   
ArithmeticCheck:
0.305 = 0.305 = 0.305

23. 2
RISE AND FALL METHOD
Example:
Thefollowingconsecutivereadingsweretakenwithadumpylevelalongachainlineata
commonintervalof15m.Thefirstreadingwasatachainageof165mwheretheRLis
98.085.Theinstrumentwasshiftedafterthefourthandninthreadings
3.150, 2.245, 1.125, 0.860, 3.125, 2.760, 1.835, 1.470, 1.965, 1.225, 2.390 and 3.035
E
FindtheRLofthestationpointsusingtheCollimationSystemandtheRiseandFall
System
Note:
Fourthandninthreadingsarechangepoints,sothefourthreadingistheforesightandthe
fifthreadingisthebacksight.Similarly,theninethreadingistheforesightandthetenth
readingisthebacksight

24. 2
PROFILE LEVELLING
•Profilelevellingshowsaprofilethatisalinedepictinggroundelevationsataverticalsection
alongasurveyline.Thisisnecessarybeforearailroad,highwaytransmissionline,sidewalkor
sewerlinecanbedesigned.
•Usuallyalineoflevelisrunalongthecenterlineoftheproposedwork.Levelistakenevery15
mor30mintervalatcriticalpointswherethereissuddenchangeoflevelsatthebeginningor
endofcurve.
•Theobjectiveistoplotaccuratelytheelevationofthepointsalongthelineoflevels.
•Itisnecessarytotakestaffreadingsalongthecenterline,bookthemproperlyinthelevelbook,
computetheRLofdifferentpointsandapplysuitablearithmeticchecks.
•ItisalsonecessarytostartfromBMofknownRLorpointsofRL.
•Itisnecessarytoplottheprofileorlongitudinalsectiontoshowthedistortionsoftheground.
•Afterthelongitudinalorprofilesectionisdrawn,itisnecessarytohaveasmoothsurfaceknown
asagradelinetobelaterusefor1.AmountofCutandFill,2.Balancingthecutandfill,3.
Keepingtheslopeswithinallowablelimit.

25. 2
PROFILE LEVELLING
1
2

26. 2
PROFILE LEVELLING
Example:
Thelevellingshowninthefilesheetgivenbelowwasundertakenduringthelayingoutof
asewerline.Determinetheheightofthegroundateachobservedpointalongthesewer
lineandcalculatethedepthofthetrenchatpointXandYiftheseweristobehavea
gradientof1in200downwardsfromAtoBandistobe1.280mbelowthesurfaceA.

27. 2
PROFILE LEVELLING
Back sight Inter sight Foresight Distance ( m) Remarks
3.417 B.M. 98.002
1.390 1.774 0 Point A
1.152 20
3.551 1.116 40 Point X
0.732 1.088 60
2.384 3.295 80
1.801 100
1.999 120 Point Y
1.936 2.637 140 Point B
1.161 B.M. 100.324

28. 2
PROFILE LEVELLING
Back
sight
Inter
sight
Foresight Rise Fall R.L. R.L. of
sewer
Distance
( m)
Remarks
3.417 98.002
1.390 1.774 1.643 99.645 98.365 00 A
1.152 0.238 99.883 20
3.551 1.116 0.036 99.919 98.165 40 X
0.732 1.088 2.463 102.382 60
2.384 3.295 2.563 99.819 80
1.801 0.583 100.402 100
1.999 0.198 100.204 97.765 120 Y
1.936 2.637 0.638 99.566 140 Point B
1.161 0.775 100.341 B.M. 100.324
Ʃ13.410 Ʃ11.071Ʃ5.738Ʃ3.399
ƩB.S -ƩF.S = 13.410 –11.071 = 2.339 ƩRise -ƩFall = 5.738 –3.399 = 2.339
Last R.L -First R.L = 100.340 –98.002 = 2.339

29. 2
PROFILE LEVELLING
99.645
99.883
99.919
102.382
99.819
100.402
100.204
99.566
95
97
99
101
103
105
0 20 40 60 80 100 120 140 160
Elevation
Distance ( m)
RL vs Distance

30. 2
FLY LEVELLING
•Thepermanentbenchmarkmaybelocatedfarawayfromthestartingpointoftheproposed
areasurvey.So,flylevellingshouldbedonetoconnectthebenchmarkwiththestartingpoint
oftheworkinordertolocateitsRLandthencalculatetheRLsofthedifferentpointalongthe
alignment.
Temporary/
Permanent BM
Starting Point of
Survey without
BM
BS FS
BS FS
BS FS
BM

31. 2
FLY LEVELLING
ƩB.S -ƩF.S = 9.840 –14.475= -4.635 ƩRise -ƩFall = 1.005 –5.640= -4.635
Last R.L -First R.L = 245.915 –250.550 = -4.635
Station BS IS FS Rise Fall R.L. Remarks
BM 0.955 250.550 On Benchmark
1.250 2.150 1.195 249.355
0.785 1.7 1.760 0.510 248.845
1.535 2.055 1.270 247.575
1.260 0.835 0.700 248.275
0.675 0.955 0.305 248.570
1.275 1.505 0.830 247.750
1.655 2.050 0.775 246.975
0.450 2.160 0.505 246.470
A
1.005 0.555 245.915 Starting Point of
Survey
Total 9.480 14.475 1.005 5.640

32. 2
FLY LEVELLING
ƩB.S -ƩF.S = 9.840 –14.475= -4.635 ƩRise -ƩFall = 1.005 –5.640= -4.635
Last R.L -First R.L = 245.915 –250.550 = -4.635
Station BS IS FS Rise Fall R.L. Remarks
BM 0.955 250.550 On Benchmark
1.250 2.150 1.195 249.355
0.785 1.7 1.760 0.510 248.845
1.535 2.055 1.270 247.575
1.260 0.835 0.700 248.275
0.675 0.955 0.305 248.570
1.275 1.505 0.830 247.750
1.655 2.050 0.775 246.975
0.450 2.160 0.505 246.470
A
1.005 0.555 245.915 Starting Point of
Survey
Total 9.480 14.475 1.005 5.640

33. 2
CROSS-SECTIONAL LEVELLING
•Thecrosssectionsaretakenperpendiculartothecenterlineofthealignmentatsomeregular
intervals(say20m,40m,etc.).Thepurposeofcrosssectionallevellingistoknowthe
undulationofthegroundsurfacetransversethecentreoftheroad.Thelengthofcrosssection
dependsuponthenatureofthework.Incaseofordinaryworkthelengthmaybe20or40m
oneachsideofthecenterline.Thelevelsaretakenatanintervalof5moneachside.
Additionalreadingsmaybetakenifthenatureofthegroundsurfacesuddenlychanges.
Stations
L = Position of Levels C.P = Change Points

34. 2
CROSS-SECTIONAL LEVELLING
C/S -1
C/S -2
C/S -3
C/S -4
C/S -5
C/S -6
C/S -7
15
10
5
0
20
5
10
15
20
Right
Left
Direction of Survey

35. 2
CROSS-SECTIONAL LEVELLING
ƩB.S -ƩF.S = 0.760 –1.525= -0.765 ƩRise -ƩFall = 3.210 –3.975= -0.765
Last R.L -First R.L = 245.150 –245.915 = -0.765
Cross Section at Chainage O
Distance ( m )
BS IS FS Rise Fall RL Remarks
LeftCenterRight
0 0.760 245.915R.L obtained
from Fly
Levelling
5 1.875 1.115 244.800
10 2.360 0.485 244.315
15 0.985 1.375 245.690
20 1.375 0.610 246.300
5 2.015 244.660
10 1.550 0.465 1.640 245.125
15 0.790 0.760 245.885
20 1.525 0.735 245.150
Total 0.760 1.525 3.120 3.975

36. 2
CROSS-SECTIONAL LEVELLING
ƩB.S -ƩF.S = 0.760 –1.525= -0.765 ƩRise -ƩFall = 3.210 –3.975= -0.765
Last R.L -First R.L = 245.150 –245.915 = -0.765
Cross Section at Chainage O
Distance ( m )
BS IS FS Rise Fall RL Remarks
LeftCenterRight
0 0.760 245.915R.L obtained
from Fly
Levelling
5 1.875 1.115 244.800
10 2.360 0.485 244.315
15 0.985 1.375 245.690
20 1.375 0.610 246.300
5 2.015 244.660
10 1.550 0.465 1.640 245.125
15 0.790 0.760 245.885
20 1.525 0.735 245.150
Total 0.760 1.525 3.120 3.975

37. 2
CROSS-SECTIONAL LEVELLING
246.3
245.69
245.69246.3245.915
244.66
245.125245.885
245.15
-25 -20 -15 -10 -5 0 5 10 15 20 25
Elevation in Meters
Distance in Meters
Cross Sectional Levelling
Datum 240 m
5L10 L15 L20 L Center 5 R 10 R 15 R 20 R