UMEC,BCPII ENGINEERING SURVEYING

UMEC,BCPII ENGINEERING SURVEYING

Natukunda Nathan,[0772-883239,0704-983239,[email protected] ]

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3.0 LEVELINGDefinition of Leveling:Leveling is the process of measuring the differences in elevation between two or more points. OR Leveling is the process by which relative heights of a number of points are determined.TERMINOLOGIES USED IN LEVELING:

1. DATUM:This can be any reference surface above which heights of other points can be determined. In practice, this is not a plane surface, but is slightly irregular surface that approximates to mean sea level, and is everywhere perpendicular to the direction of gravity.

2. ASSUMED DATMUM:This is any datum chosen to avoid inconveniences and hardship that may arise in relating the work to the Ordinance Datum. 3. BENCH MARK (BM):These are fixed points of known heights above the reference datum used, from which heights of other points above datum can be determined.4. TEMPORARY BENCH MARK (TBM):This is a benchmark set up by a surveyor for his own use for a particular task.5. ARBITRARY BENCH MARK (ABM):This is a BM that is not related to any datum, and it is always assigned any convenient value say 100m above what nobody knows.



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6. HORIZONTAL LINEA horizontal line at a point is that line which is perpendicular to the direction of gravity at that point.

7. A LEVEL LINE;A level line is that of uniform height relative to the mean sea level (i.e reference datum). Because the mean sea level is curved, a level tine is also curved, and every where perpendicular to the direction of gravity.

8. LEVEL SURFACE:This is a surface that is everywhere perpendicular to the direction of gravity. It therefore follows that a level line ties on a level surface.NOTE: A level surface is not a plane surface but a spherical surface.



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9. LINE OF COLLIMATION (LOC):This is a true horizontal line of sight, which passes through the optical centre of the telescope of the level.10. HEIGHT COLIMATION (HOC);This is the height of the line of collimation above the reference datum.

11. PLANE OF COLLIMATION:Is the plane generated by rotating the L.O.C about the vertical axis of the telescope.12 REDUCED LEVEL (RL)Is the height of a point relative to the reference datum.13. BACK SIGHT (BS):Is the first sight or reading taken for every instrument setup. It is taken from point of known/assumed height (RL) and at a change point /14. FORE SIGHT (FS): ' Is the last reading taken for every instrument set up. It is taken at a change point and finally at the end of leveling operation.15. INTERMEDIATE SIGHT (IS)Is any sight or reading take between" a BS and a FS.16. CHANGE POINT (CP):This is a point where we take both a FS and a BS with two different consecutive instrument positions respectively. The foot of the staff remains at the same CP until when the two readings FS and BS are taken.



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17. Mean sea level (MSL) is the mean level of the sea as determined at a selected place from observations over a period of time ,used as a datum surface for leveling work. OR MSL is the level datum line taken as the reference plane.

EQUIPMENTS USED IN LEVELING.The equipments used in leveling are as follows: A level,, a staff and a tape.

A LEVELA level is an instrument used in the process of measuring the differences in elevation between two or more points.Levels are categorized into three groups.

i). Dumpy levelii). Tilting level

iii). Automatic level

1. DUMPY LEVEL:Permanent adjustment to the dumpy levelFor a dumpy level to function properly , it is necessary that the axis of rotation of a telescope is vertical when the bubble is central bubble. And the line of collimation is perpendicular to this axis. The following tests i.e. Adjustment of a bubble tube and Adjustment of line of sight , will reveal whether or not a correction is necessary, if so the adjustments is referred to, as ҅҅permanent adjustment,, though not permanent .



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TEMPORARY ADJUSTMENTS OF ADUMPY A LEVEL: (Adjustment of a bubble tube)The distinguishing feature is that the telescope is rigidly attached to an axis which rotates in a sleeve (part of a tribuach).

The process by which the instrument is made in a suitable state on its tripod stand and ready to make observations is termed temporary adjustments'

i) Setting up the tripod:The tripod must be firmly placed on a stable ground, with its top family set in a horizontal plane.

On a flat ground, the length of the legs should be equal, and their ends on the ground equidistant from each other,

While on slopping ground, one leg will be shorter and point uphill, while the other two legs point downhill at equal intervals, (fig below)

• Remove the level from its case and secure it firmly on the tripod head.There is captive bolt to be screwed up into the underside of the instrument. It isfrustrating when setting up and you find that the level and tripod do not marry.



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ii) Leveling:The level shall have three foot screws, (fig below).

a) The telescope is placed parallel to two fort screws (2) and (3) in (a) above.• The bubble is centered using these two screws (2) and (3)• To achieve the centering, both screws (2) and (3) are turned

simultaneously at the same speed but in opposite directions.• It is to be noted that the bubble moves in the same direction are screw (2) (i.e left

thumb).b) When the bubble is centered turn the telescope through an angle of 900 i.e to the direction of screw (1).Check that the bubble is centered while in this position using screw (i).c) Turn the telescope back to its initial position (a), and re-level if necessary and then turn it through an angle of 180° as in fig (c) above.If the bubble remains centered in this position, then it is said to have "traversed" and the telescope can be pointed to any direction and ready for use.But if the bubble does not traverse, then repeat the whole process again with a lot of care. If the bubble does not traverse this time, then there should be some permanent adjustment problem. (iii) Parallax Removal: The process of parallax removal is the same for all telescopes used in different levels.

• The telescope is focused to a light background (i.e blue sky or white sheet of paper).

• The eyepiece ring is then turned until when the reticule pattern is seen black and sharp.



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Target observation• Once the instrument has been set, leveled and parallax removed, the next stage is

to sight to the target.• Aim at the target and lock the instrument.• Focus it using the focusing ring in order to have a clear image of the target.• Bisect the target properly with the cross hair using the slow motion screw.• Take the cross centre hair reading.

2. TILTING LEVEL:

Unlike the dumpy level, the tilting level needs only the vertical axis to be approximately vertical for the instrument to be in good adjustment. This is achieved by centering the small circular bubble at each instrument set up using ball & socket joint or foot screws.

Before a reading is taken, the line of sight must be made horizontal by centering the main bubble using tilting screw. The telescope has no rigid attachment with the tribuach.

Permanent adjustment of the tilting levelThere is only one permanent adjustment necessary for this instrument to be in good adjustment

i.e the bubble tube axis must be made parallel to the telescope axis so that when the bubble is central, the line of sight is horizontal.



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3. AUTOMATIC LEVEL:There is now a great range of automatic level in the market. The spirit level is no longer used to set the horizontal L.O.C. If the standing axis is set approximately vertical in a similar manner to that of tilting level, the system of compensations automatically corrects for any slight variation from the vertical.

LEVELLING STAFFThere are two basic types of staves:a) WOODEN STAFF

Made from well-seasoned mahogany.• do not suffer from temperature variation.

Affected by waterb) METAL STAFF:• Made from aluminum alloy.

• Do suffer from temperature variation.• Not affected by water.STAFF ACCESSORIES:a) STAFF BUBBLE:This is a circular spirit level, attached to the staff in order to enable the staff to improve on the verticality of the staff while observation is being made. b) STAFF HOLDER:These are clamped to the staff to make holding easier especially in windy condition.c) CHANGE PLATE:This is a triangular steel plate, used where a change point occurs on a soft ground to form a stable base.



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EXAMPLE OF ALEVELING STAF

=2.050

=2.033

=2.002

=1.978

=1.960

=1.915



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FIELD PROCEDURE IN LEVELING:

It is required to find the reduced levels of points A, B, C,D & E. Leveling started from (BM) and closed at (TBM).

1. The level is set up at a convenient position I1, and a BS of 2.191m taken to theBM.

2. The staff is moved to points A and B, and the ISs 2.507m & 2.325 m taken respectively.

3. Because of the nature of the ground, a change point is needed in order to reach point D. The staff is therefore moved to point C (CP) and a FS reading of 1.496m taken.

4. With the staff still at C (CP), the instrument is moved to a new station I2 and a BS reading of 3.019m is taken to a staff at C.

5. The staff is moved to point D and an IS reading of 2.513m taken.

6. The staff is then moved to point E (CP) and a FS reading of 2.811m taken.



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7. Finally the level is moved to station Is and a BS of 1.752m taken to E and a FS of 3.817m taken to the TBM.

*The first and last staff positions are always at points of known heights.*This is to allow to detect the "closing error".*When booking leveling in more than one page, the last reading in a page should be booked as a FS and the same point repeated as a BS reading in the next page.

BOOKING & REDUCED LEVEL CALCULATIONS:There are two known methods for booking and deduction of the readings, namely:

i. The "Rise and fall" method.ii. The ''Height of Collimation" method.

RISE AND FALL METHOD:

BS IS FS RISE FALL RL REMARKS

2.91 49372 BM(49.872m)

2.507 0316 49.556 A

2.325 0.182 49.738 B

3.019 1.497 0.829 50.567 C(CP)

2.513 0.506 51.073 D1.752 2.811 0.298 50.775 E(CP)

3.817 2.065 48.710 TBM(48.719m)

∑:6.962 ∑:8.124 ∑:1.517 ∑:2.679 49.872

6.962 1.517 48.710

+1.162 +1.162 +1.162 TABLE I

Explanation:• Each line of level book corresponds to a staff position as indicated in remarks

column.• When calculating the rises or falls, the figures in the FS or IS columns must be

subtracted from the figures in the line immediately above, this is either in the same column or to the left. A positive difference is recorded as a rise, while a negative difference is recorded as a fall.



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• At a CP, the FS is subtracted from the IS or BS in the line above and the BS on the same line as the FS is then used to continue the calculation with the next IS or FS in the line below.

• The summations of BS, FS, RISES & FALLS are obtained and entered at the foot of the respective columns. The arithmetical checks must be applied.

Arithmetical checks∑ (FS) - ∑ (BS) - ∑ (FALL) -∑ (RISES) = F1RSTRL - LASTRL

*MISCLOSURE:[The obtained RL of the closing station]-[The actual RL of that very station] is called the"misclosure".

Referring back to table I showing the rise and fall booking method, the mis closure is obtained as:Mis closure = Obtained RL of TBM - Actual RL of TBM

= 48.710 - 48.719 = -0.009m.•ACCURACY:The accuracy is indicated by the mis closure. There is always an acceptable limit for mis closure, called the "Tolerance (E)" given by:E = ±(Fd√N) m where;F is a factor varying from 1 to 3, depending on site & weather conditions.d is usually taken as 0.003m, andN is the number of instrument positions.For example our allowable mis closure (error) from table I vary from

±0.005m to ±0.016m, depending on the value chosen for F.NB: When the mis closure (closing error) is greater than the allowable

error (tolerance), the leveling has to be repeated. If however themisclosure (closing error) is less than the allowable error(tolerance)/ the misclosure should be distributed as seen below.



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*ERROR DISTRIBUTION:With reference to table I, our mis closure is -0.009m and it is within the acceptable limit of ±0.005m to ±0.016m. This mis closure is to be distribute throughout the RLs of all points with the exception of the opening bench mark.*The usual way of error distribution is to apply an equal but cumulative amountof mis closure to each instrument position.Note: The applied correction takes the opposite sign of the mis closure. As with our example here, the mis closure is -- 0.009m. There are altogether three instrument stations and the applied correction is as below:

Correction = . , where: n =Number varying stations.

E = error, N=total number stations used.

STATION INITIAL RL ADJUSTMENT ADJUSTED RL REMARKS

BM 49.872 BM(49.872)

A 49.556 1/3(0.009)=0.003 49.559 A

B 49.738 1/3(0.009)=0.003 49.741 B

C(CP) 50.567 1/3(0.009)=0.003 50.570 C (CP)

D 51.073 2/3(0.009)^0.006 51.079 D

E(CP) 50.775 2/3 (0.009) = 0.006 50.781 E(CP)

TBM 48.710 3/3(0.009)=0.009 48.719 TBM



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HEIGHT OF COLLIMATION METHOD:

BS IS FS HOC RL REMARKS

2.191 52.063 49.372 BM(49.872)

2.507 49.556 A

2.325 49.738 B

3,019 1.496 53.586 50.567 C(CP)

2.513 51.073 D

1.752 2.811 52.527 50.775 E(CP)

3.817 48.710 TBM

∑6.962 ∑7.345 ∑8.124 49.872

6.962 48.710

+1.162 +1.162TABLE II

Explanation: • Each line of a level book corresponds to a staff position as indicated in the

remarks column.• The height of collimation is determined per instrument set up. For every

instrument set up, a BS reading is added to the RL of that very station to which it is taken in order to get the H.O.C.

E.g At I1, HOC1 - RL(BM) + BS(BM) = 49.872 + 2.191 = 52.063m.At l2 HOC2 = KL(C) + BS(C) = 50.567 + 3-019 = 53.586m.At l3 HOC3 = RL(E) + BS(E) = 50.775 + 1.752 = 52.527m. • After the HOC is determined, the RL of any point is got by subtracting its reading

(IS or FS) from the HOC.• Summations of BS and FS are obtained and entered at the foot of the respective

columns, and the arithmetical check should be applied.

Arithmetical checks ∑(FS) - ∑ (BS) = F1RSTRL - LASTRL.

8.124-6.962 = 49.872 – 48.710 +1.162 = +1.162



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Additional check : The sum of each collimation height ,multiplied by the number of RL obtained from it = to the sum of all intermediates , FSs and RLs excluding the first RL.Sum of [H.I x No of RLs obtained from it]= sum of [IS+FS +RLs except first RL][52.063 x 3 + 53.586 x 2 + 52.527 x 1] =[7.345 + 8.124 + 300.419] 315.888 = 315.888

The misclosure, accuracy and error distribution are all the same as wasseen in the Rise and Fall method (i.e done the same way).* The rise and fall method, although involves more arithmetic, is preferred since it checks all reduced levels, compared to HOC method where intermediate RLs are unchecked.*On the other hand, the HOC method is quicker and simpler and is preferred where a lot of readings (IS) are taken from one instrument station.

Home work:Qn1.The group of figures below refer to staffreadings taken with alevel from instrument stations A toE . the first and lasting reading in each group are back sight and fore sight respectively.The back sight from from station A was taken with a staff held on a BM at 204.110m above datum.A: 2.680, 0.875, 0.987, 0.430B: 1.665, 1.440, 0.625C: 1.010, 1.690, 1.225D: 2.445, 3.575, 3.880, 2.880E: 2.735, 2.005, 2.390Book the readings by rise and fall method and reduce levels of each staff station.



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MISCELLANEOUS:ONE SET UP LEVELLING:

This is leveling carried out with only one instrument position; and say many ISs taken. Eg Leveling at a building site. There is no change point in this type of leveling.

SERIES/CONTINOUS LEVELING:

This is leveling carried out with more than one instrument position. This involves many change points. Series leveling is convenient where there are some obstacles or where leveling is to cover quite a large area.

FLYING LEVELING:

This is leveling or readings taken for the purpose of checking a series of levels already taken in greater detail. Flying levels are taken without inter sights, and every point is treated as a change point. The system is used between two points of known RLs. Leveling can be run back through the CPs already used or via new ones and to close onto the starting point, or some other point of known height. To reduce errors BS and FS distances should be kept equal.

TRIAL LEVELING:

These are a series of levels taken merely to determine the difference in heights between two points. It is usually carried out as a reconnaissance survey before a more detail survey is carried out. `

INVERT LEVELLING:Normally the levels of interest to the surveyor are below the L.O.C, but this is not always the case. For example when leveling under a bridge or checking the levels of the underside of the roof or taking the levels of the ceiling or to continue the leveling operations over an obstruction.To overcome this problem we need to have what we call the "inverted staff position."



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INVERTED STAFF POSITION:

To obtain levels of points above the L.O.C, say underside of the bridge. The staff is held upside down in an inverted position, with its base on the elevated points. When booking an invested staff reading, it is entered in the leveling table with a "minus sign", and the calculation is carried out in the normal way, taking the sign into account.

Illustration:*Let us look at the fig. below to illustrate leveling on the underside of a bridge.

Explanation:Each inverted reading is recorded as a negative reading , the rise and fallcomputed accordingly.

EgThe rise from TBMA to pt X is given by: BS - IS =1.317 - (-3.018) = +4.335m.The fall from Z to TBMB is given by: IS - FS = -3.602 -1.496 = -5.098m. The table below shows the booking of the above reading.



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INVERTED STATF-BOOKING (RISE&FALL)

BS IS FS RISE FALL RL REMARKS

1.317 20.798 TBMA(20.798m)

-3.018 4.335 25.133 X

1.427 2.894 5.912 19.221 CP

-2.905 4.332 23.553 Y

-3.602 0.697 24.250 Z

1.496 5.098 19.152 TBMB(19.152m)

∑2.744 ∑4.390 ∑9.364 ∑ll.010 20.798

2.744 9364 19,152

+1.646 +l.646 +1.646

TWO PEG TEST OF ALEVELING INSTRUMENTWhen the bubble of the level is centered, it is not a guarantee that line of sight is horizontal. It is always good to carry out the two-peg test to find the presence and magnitude of the collimation error ҽ. This is done as below in Fig1 and Fig2



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About Fig 1: On a relatively flat site establish two pegs A and B about 60m apart and set up

the instrument at I1 ,appoint half – way between them.(such that d1= d2=d=30m) After careful leveling and focusing , sight on staff held vertically at A and

record reading a1 .repeat with the staff held at B and record reading b1

Assuming the line of collimation is not horizontal but inclined at an angle ҽ . Then ҽ will be the collimation error of the instrument in radians.

Let the true difference in level between A and B be ∆H ∆H = (a1-d1e) – (b1-d2e)

= [ a1-d1e- b1 +d2e] But d1 = d2 =d

∆H =( a1-b1)………………………………………………* Equation * shows that the collimation error e does not affect the true difference in

height , provided the instrument is set mid way. About Fig2: The instrument is shifted to I2, the distance d3 away from B on Line AB produced. Such

that d1=d2=d3=30m. Reading a2 and b2 are recorded at A & B respectively. Let the true difference in level between A & B be ∆H ∆H=[a2-(d1+d2+d3)e] – [b2-d3e] but d1=d2=d3=d

=a2-d1e-d2e-d3e-b2 +d3e = (a2-b2)-(d1+d2)e = (a2-b2)-2de …………………………………………….**

By equating eqn * and **



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a1-b1 = a2 –b2-2de. 2de =( a2-b2) –(a1-b1)

e = ( ) ( )

If e ≤ │0.000005│ then the instrument is good enough to be used. If e is big , with instrument still at I2 the line of sight is lowered down , using adjusting screw until a reading a2-(d1+d2 +d3)e is observed on a staff at A. this will however cause the bubble to move to the centre. This procedure is repeated until when the absolute value is e≤│0.000005│.

Note: if e is +ve , it implies that the line of sight is inclined up wards and if e is –ve ,then it implies that line of sight is inclined down wards.

USES OF LEVELING1. Determination of heights.2. Determination of longitudinal and Cross-Sections e.g construction of

roads,Canals, Chanels, Sewers, Railway lines.3. Contouring: –For mapping purposes.

-For determination of volumes of Earth works

SECTIONSDetermination of Sections[Longitudinal & Cross-sections]One of the most common application of leveling is sectioning.Always Vertical sections are drawn to show clearly the profile of the ground , when ever narrow works of long length are to be constructed .e.g Roads ,drains, Canals e.t.cThere are two kinds of sections.

1) . Longitudinal Section: is the vertical section along the centre line of the works.

2) . Cross-section: is the Vertical Section at right angles to the centre line of the

works.The information obtained from the sections gives data for:

i) Determination of suitable gradients for the works.ii) Calculation of volumes of earth to be removed or broughtiii) Depth of cutor fill required .



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Longitudinal SectionsBefore any section can be drawn some field work must be carried out.Level readings must be taken along the centre line , at every tape length and at all points of chainage of the gradient.All points must have a running chainage. [From chainage Zero to the last chainage].For long sections a surveyor and three assistants are required.

i). A surveyor takes reading and books.ii). One assistant acts as a staff man.

iii). Two assistants acts as chain men:- for measuring, ranging, paging all tape lengths.Transfer of levels is done by a nearby BM to the page of zero chainage. All measurements start at a page of zero chainage. And one the booking methods are used to reduce the levels [Rise and Fall or Height of Collimation method]As in all surveying work, a check must be provided.

CALCULATION FOR DEPTH OF CUT OR FILL.

Depths of cut or fill are calculated or scaled off on the section.Formation level of the works is the level to which the volume of the earth is excavated or deposited to accommodate the works.Depth of excavation is the distance between the surface and formation level.Procedures for calculation of cut or fill.

i) Calculate the reduced level at each chainage point.ii) Calculate the proposed level of works [formation level ] at each chainage point.iii) Find the difference between (i) and (ii) . where the reduced level is higher than formation

level, the cut must be made and where the reduced level is lower than the formation level , a fill must be made.



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EXAMPLE1.levels were taken along the centre line of the proposed roadway at 25m interval gave the readings shown in the table below. The reduced level of the formation at A is 39.20m,the road is to have arising gradient of 1 in 40 between A and B and 1 in 16 between B and C. Reduce all the levels and indicate the depth of cut or fill at each chainage point.BS IS FS CHAINAGES REMARKS2.300 0 A(RL40.180M)

2.010 251.610 501.310 75

3.950 1.160 100 B2.690 125

3.090 0.330 1500.510 175 C

SOLUTIONBS IS FS RISE FALL RL FML CUT FILL Remarks2.300 40.18 39.20 0.980 0ARL[ 40.180]

2.010 0.29 40.47 39.825 0.645 251.610 0.40 40.87 40.45 0.420 501.310 0.30 41.17 41.075 0.095 75

3.950 1.160 0.15 41.32 41.700 0.380 100 (B)2.690 1.26 42.58 43.263 0.683 125

3.090 0.330 2.36 44.94 44.825 0.115 1500.510 2.58 47.52 46.388 1.132 175( C)

Formation level = invert level at A ± C/40Ch 25: Fl =39.2 + 25/40 = 39.825Ch 50: Fl =39.2 + 50/40 = 40.45Ch 75: Fl =39.2 + 75/40 = 41.075Ch 100: Fl =39.2 + 10/40 = 41.700Formation level = invert level at B + C/16Ch 125: Fl =41.700 + 25/16 = 43.263Ch150 : Fl =41.700 + 50/16 = 44.825

Ch 175: Fl =41.700 + 75/16 = 46.388



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Note:The depth of cut or fill = RL – FMLExample 2.The table below shows the readings obtained during the leveling of proposed works along the line A-B.the leveling commenced on the BM number 28 and ended on BM number 29.Reduce all the levels and indicate the depth of cut or fall at each chainage point.BS IS FS DISTANCE REMARKS1.370 BM28(91.085m)2.795 0.035 0 A

3.040 201.765 40

3.865 0.565 602.095 80 B

2.240 1.0750.385 BM29(99.295m)

SOLUTIONBS IS FS RISE FALL RL FML CUT FILL Remarks1.370 91.085 BM289(91.085)2.795 0.035 1.335 92.420 92.420 - - 0(A)

3.040 0.245 92.175 93.420 1.245 201.765 1.275 93.450 94.420 0.97 40

3.865 0.565 1.200 94.650 95.420 0.77 602.095 1.770 96.420 96.420 - - 80(B)

2.240 1.075 1.020 97.4400.385 1.855 99.295 BM29(99.295)

Rl at A= 92.42mRL at B = 96.42m

Thedifference = 96.420 – 92.420 = 4m Gradient of AB =∆y/∆x = 4/80 = +0.05 = 1 in 20 Formation level = invert level at A + C/20 Ch 20: FL = 92.420 + 20/20 = 93.420

Ch 40: FL = 92.420 + 40/20 = 94.420Ch 60: FL = 92.420 + 60/20 = 95.420Ch 80: FL = 92.420 + 80/20 = 96.

UMEC,BCPII ENGINEERING SURVEYING

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