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levelling applications

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of all the surveying operations used in construction levelling is the most common practically every aspect of a construction project requires som app;ication of the levelling process the general are as follows.

sectional 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 project , the route centre - line is set out using pegs at 10 m , or 30 m intervals . levels are then taken at these peg positions and at critical point such as sudden changes in ground profiles road crossing , ditches , bridges , culverts , etc , A plot of these elevations is called a longitudinal section,.

when plotting the vertical scale is exaggerated compared with the horizontal , usually in the ratio of 10 : 1 the longitudinal section is then used in the vertical design process to produce formation levels for the proposed route design

whilst the above process produces information along centre - line only , cross - sectional levelling extends that information at 90 ُ to the centre - line for 20-30 m each side . at each centre - line peg the levelsare taken to all point of interest on either side . where the ground is featureless , levels at 5 m intervals or less are taken ,in this way a ground profile at right angles to the centre - line is obtained , when the design template

longitudinal section of proposed route

showing the road details and side slope is plotted at formation level , a cross-sectionaal area is produced , which can later be used to compute volume of earthwork . when plotting cross-section the vertical and horizontal scales are the same , to permit easy scaleing of the area and side slopes

from the above it can be seen that sectional levelling also requires the measurement of horizontal distance between the point whose elevations are obtained . As the process involves the observation of many points , it is important to connect to existing BMs at regular intervals . in most cases of routs construction, one of the earliest tasks is to establish BMs at 100 m intervals throughout the area of interest . levelling which does not require the measurement of distance , such as establishing BMs at known positions , is sometimes called , fly levelling .


A contour is a horizontal curve connecting points of equal elevation . contours graphically represent , in a two-dimensional format on a plan or maap , the shape or morphology of the terrain . the vertical distance between contour lines is called the contour interval . Depending on the accuracy required , they may be interval chosen depends on :

(1) the type of project involved : for instance , contouring an airstrip requires an extremely small contour interval .

(2) the horizontal separation between contour lines indicates the steepness of the ground . close spacing defines steep slopes , wide spacing gentle slopes .

(3) Highly irregular contours define regged , often mountainous terrain .

cross section 

(4) concentric closed contours represent hills or hollows , depending on the increase or in elevation .

(5)  the slope between contour line is assummed to be regular .

(6) contour lines crossing a stream from V,s pointing upstream .

(7) the edge of a body of water forms a contour line .

contour are used by engineers to :

(1) construct longitudinal sections and cross- sections for initial investigation .

(2) compute volumes .

(3) construct route line of constant gradient .

(4) delineate the limits of constructed dams , road , railways , tunnels ,etc 

(5) delineate and measure drainage area ,

if the ground is reasonably flat , the optical level can be used for contouring using either the direct or indirect methods , in steep terrain it is more economical to use heighting ,as outlined later . 

sources of error

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all measurements have error in the case of levelling these errors will be instrumental observational and natural 

instrumental errors

the main source of instrumental error is residual collimation error . As already indicated , keeping the horizontal lengths of the backsights and foresights at each instrument position equal will cancel this error ,

where the observational distance are unequal , the error will be proporational to the difference in distance .

the easiest approach to equalizing the sight distance is to pace backsight to instrument and then set up the foresight change point the same number of pace away from the instrument .

2- parallax error has already been described .

3- staff graduation errors may result from wear and tear or repairs and the staffs should be checked against a steel tape , zero error of the staff , caused by excessive wear of the base , weill cancel out on backsight and foresight difference however , if two staffs are , errors will result unless calibration corrections are applied .

4- in the case of the tripod , loose fixing will cause twisting and movement of the tripod . ovvertight fixing makes it difficult to open out the tripod correctly . loose tripod shoes will result in unstable calibration corrections are applied .

4- in the case of the tripod will cause twisting and movement of the tripod . overtight fixing make it difficult to open the tripod correctly , losse tripod shoes will also result in unstable set-up .

observational errors

levelling involves vertical measurements relative to a horizontal plane so it is important to ensure that the staff is held strictly vertical ,

it is often suggested that one should rock the staff and forth in the direction of the line of sight and accept the minimum reading as the truly vertical one . however , this concept is incorrect when using a flat-bottomed staff on flat ground , due to the fact that staff is not being tilting about its face , thus it is perferable to use a staff bubble , which should be checked frequently with the aid of a plumb - bob .
(2)  there may be errors in reading the staff , particularly when using a tilting level which gives an inverted image , these errore may result from inexperience ., poor observation conditions or overlong sights limit the lengh of sight to about 25-30 m .
to ensure the graduations are clearly defined .

(3) ensure that the staff is correctly extended or assembled in the case of extending staffs listen for the applies to jointed staffs.

(4) Do not move the staff off the CP position , particularly when turning it to face the new instrument position , Always use a well defined and stable position for CPs . levelling plates , should be used on soft ground

the effect of rocking the staff on readings

levelling plate

5- Avoid sttlement of the tripod , which may alter the height of collimation between sights or tilt the line of sight , set up on firm ground , with the tripod feet firmly thrust well into the ground , on pavements . locate the tripod shoes in existing cracks joins , in precise levelling , the use of two staffs helps to reduce this effect
observers should also refrain from touching or leaning on the tripod durring observation.

6 - booking errors can of course ruin good field work .Neat , clear , correct booking of field data is essential in any surveying operation. typical booking errors in levelling are entering the values in the wrong columns or on the worng line . and making airthmetical errors in the reducation process . very often the use of pocket calculators simply enables to avoid this error source , use neat ,  legible figures : read the booked value back to the observer and have them check the staff reading again ; reduce  the data as it recorded .

(7) when using a tilting level remember to level the tubular bubble with the tilting screw prior to each new staff reading . with the automatic level carefully centre the circular bubble and make sure the compensator is not sticking .

residual compensator errors are counteracted by centring the circular bubble with the instrument throughout the levelling .

natural errors

(1) Curvature and refraction have already been dealt with . their effects are minimized by observation distances to backsight and foresight at each set-up and readings more than 0.5 m above the ground .

(2) wind can cause instrument vibration and make the staff difficult to hold in a steady position. precise levelling is impossible in strong winds . in tertiary levelling keep the staff to its shortest length and use a wind break to shelter the instrument.

(3)  heat shimmer can make the staff reading difficult if not impossible and may make it necessary to delay the work to an overcast day . in hot sunny climes , carry out the work early in the morning or in the evening ,

careful consideration of the above error source , combined with regularly calibrated equipment , will ensure the best possible results but will never precude random errors of observation.

closure tolerances

it is important to realize that the amount of misclosure in levelling can only be assessed by ;

(1) connecting the levelling back to the BM from which it started , or

(2) connecting into another BM of known and proved value .

whwn the misclosure is assessed one must then decide if it is acceptable or not . in many case the engineer may make the decision based on his/her knowledge of the project and the tolerance required .
Alternatively the permissible cirteria may be based on the distance levelled or the number of set-ups involved.

A common criterion used to assess the misclosure (E) is :

E = m(k) 2

where k = distance levelled in kilometers , m = a constant with units of millimeters , and E = the allowable misclosure in millimetres .

the value of m may vary from 2 mm for precise levelling to 12 mm or more for engineering levelling , in many case in engineering , the distance involved is quite short but the number of set- ups quite high.
in which case the following criterion may used ;

E = m (n) 2

error distribution

in previous levelling examples in this chapter misclosures have been shown , the misclosure cannot be ignored and the error must be distrbuted among the point concerned , in the case of a levelling circuit ,  a  simple method of distribution is to allocate the error in proportion to the distance levelled for instance , consider a levelling circuit commenncing from a BM at A , to establish other BMs at B, C ,D  and E - for which the heights have computed without taking the misclosure into account ,

on completing the circuit the observed value for the BM at A is 20.018 m compared , with its known and hence starting value of 20,000 m , so the levelling 0.018m . the distance levelled is 5,7 km considering the purpose of the work , the terrain and observational conditions , it is decided to adopt a value for m of 12 mm , hence the acceptable mislosure is 12 (5,7)2 = 29mm , so the levelling is acceptable .

the difference in heights is corrected by (0.018/5.7) × distance in kilometres travelled , therefore correction to AB =  - 0.005 m , to BC = - 0.002m , to DE = - 0.006 m and to EA  = - 0.002 m . the value of the BMs will then be B = 28.561 m , C = 35.003 m , D = 30.640 m . 
E = 22.829 m and A = 20.000 m .

in many instance ,a closing loop with known distance is not the method used and each reduced level is adjusted in proporation to the cumulative number of set-ups to that point from the start . consider the table 

vertical control 

below which shows the observations for a fhort section of levelling between two bench marks of known height:

(1) there are four set- ups , and therefore E = 5(4)2 = 0.010 m , As the misclosure is only 0.008 m . the levelling is acceptable .

(2) the correction per set - up is (0.008/4)  =  -  0.002 m and is cumulative as shown in the table .

principle of leveling

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the instrument is set up and correctly levelled in order to make the line of sight through the telescope horizontal . if the telescope is turned through 360 ُ . a horizontal plane of sight is swept out . vertical measurement from this plane .

using a graduated levelling staff . enable the relative elevation of ground points to be ascertained . consider , with the instrument set up approximately midway between ground point A and B . if the reducced level (RL) of point A known and equal to 100.000 m above OD 

(AOD) then the reading of 3.000 m on a vertically held staff at A gives the reduced level of horizontal line of sight as 103.000 m AOD . this sight onto A is termed a backsight (BS) and the reduced level of the line of sight is called the height of the plane of collimation ( HPC) thus ;

RLa + BS = HPC

the reading of 1.000 m onto the staff at B is called a foresight (FS) and shows the ground point B to be 1.000 m below HPC ; therefore its RL = (103.00 - 1.000) = 102.000 m AOD .

An alternative approach is to subtract the FS from the BS . if the result is positive then the difference is a rise from A to B and if negative a fall . i.e

(3.000 - 1.000 ) = + 2.000 m rise from A to B 

therefore , RLb  =  100.000 + 2.000 = 102.000 m AOD

this then is the basic concept of leveling which is further developed in .

the field data are entered into a field book that is pre-drawn into rows and columns . an example of levelling observations from a practical project, observation are booked using either the rise and fall or the HPC method .

it should be clearly noted that , in practice , the staff readings are taken to places of decimals , that is , to the nearest millimetre . however , in the following desripion only one place decimals is used and the numbers kept very simple to prevent arithmetic interfering with an understanding of concepts outlined ,

the field procedure for obtaining elevations at a series of ground point is as follows .
the instrument is set up at A, from which point a horizontal line of sight is possible to the TBM at 1A the first sight to be taken is to the staff held vertically on the TBM and this is called a 

basic principle of leveling

backsight (BS) the value of which (1.5 m ) would be entered in the appropriate column a levelling book . sight to point 2 A and 3A where further levels relative to the TBM are required sight arenintermediate (IS) and are again in the appropriate column of the levelling book . the final sight from this instrument is set up at 4A and is called the foresight (FS) it can be seen from figure that this is as far as one can go with this sight if . 

for instance the staff had been placed at X it would not have been visible and would have had to be moved down the slope , towards the instrument at A until it was visible As foresight 4A is as far one can see from A . it is also called the change point (CP signifying a change of instrument position to B . to achieve continuity in the levelling the staff must remain at exactly the same point 4A although it must be turned to face the instrument at B . it now becomes the BS for the new instrument set-up and whole procedure as before ,

thus one must remember that all levelling commences on a BS and finishes on FS with as many IS in between as are required ; and that CPs are always FS/BS . Also , it must be closed back into a known BM to ascertain misclosure error .