eee eee Ca Maha LEVELS AND LEVELLING Level: A level is an instrument by which the relative heights of different points on the surface of the earth are determined. Levelling: Levelling is the process by means of which the difference in elevation of various points on the surface of the earth is calculated Levelling Instruments: ; i)Level _ ii) Levelling staff _iii) Tape or Chain Types of Level: / i)Dumpy level _ ii) Y or Wye level ili) Cooke's reversible level iv) Cushing’s level v) Zeiss, Wild’s and Watt's modern level or Tilting level Some definition: , . | a) Level surface: A level surface may be defined as the surface which coincides with the shape adopted by the surface of a free liquid. The surface of a still lake may be considered as a level surface. b) Mean-Sea-Level (MLS.L.): It is the average elevation of the surface of the sea. In Bangladesh, the mean-sea-level at Cox’s Bazar is taken as zero. ©) Geoid: The surface of the earth at mean-sea-level is termed as geoid. ) Datum: It is the imaginary surface with respect to which the heights of different points on the earth surface are determined. * Inalmost every country the mean-sea-level is considered most suitable for datum. « The MS.L. at Cox's Bazar is the datum in Bangladesh © In levelling operation a certain datum is assumed and the relative heights of different points are calculated with respect to this datum. ¢) Reduced Level (R.L.): The elevation of any point with reference to the assumed datum is termed 2s reduced level of that point, f) Bench Mark'(B.M.): A bench mark is a fixed point on the ground of known elevation. ‘There are four types of bench mark: i) G-TS. Great Trigonometrical Survey): G.T.S. bench marks are established with high degree of precision at regular intervals throughout the country and their elevation above the M.S.L. at Cox’s Bazar are given by the Survey Department of Bangladesh. ii) Permanent.B.M.: Permanent bench marks are the fixed points of reference of known elevations between the G.T.S. bench marks given by the Bangladesh P.W.D. iii) Arbitrary B.M.: Arbitrary bench marks are the reference points whose elevations are assumed arbitrarily for small levelling works. iv) Temporary B.M.: Temporary bench marks are the reference points which are generally established at the break of any levelling work on some permanent objects. 8) Height of instrument: the elevation of the line of collimation above the datum is termed as the height of instrument. This is also known as R.L. of the line of collimation, bh) Station: A station is a point whose fcollinion elevation is to be determined, a F + Itis a point where staff reading is taken but not the point where the level is set up. Esfiment Datumhh) Change point: It is an intermediate ‘station on which two readings are taken while the position ofthe instrument is shifted, = i) Back reading: In any set up of the levelling instrument, the first staff reading on a station is termed as back reading. : / j). Fore reading: The lst staff reading on a station is termed as fore reading, —— 1) Inter reading: The reading of the intermediate station is termed as inter reading, Types of leveling: Following are the most common types of leveling, i) Fly or differential leveling ii) Check leveling ; iii) Profile or longitudinal leveling iv) Reciprocal leveling vy) Contouring i) Trigonometrical leveling vii) Precise leveling viii) Barometric leveling Purpose or objectives of leveling: i) To level a piece of ground according to a given altitude ii) To know the relative heights or depths of two adjacent place iii) To estimate the quantity of earth work for roads, canals, drains etc. iv) To provide slopes of roads, railways, canals, rivers ground, roof etc. , v) To fix up permanent B.M. with RLL. for check and reference for local leveling. Procedure of Leveling operation: 4) In figure, it is required to determine the heights of the point Pi, P2, Ps etc. ii) These heights can be determined with a reference to a bench mark P whose R.L. is known iii) At first place the level at A, after proper leveling and adjustment of the level take the staff readings at P1, P2, Ps, Ps and Cp, iv) Shift the level at B and take the staff readings at Cp, Ps, Ps, Pr, Pe, and Po. ¥) The staff is always perpendicular to the line of collimation during taking readings on these different points. This is achieved by swinging the staff backward and forward and recording the smallest reading. vi) Some times negative staff reading is taken when the ground is above the line of collimation and these readings are taken with the staff upside down. This negative reading is added to the RL. of the line of collimation to obtain the RL. of the required point, Methods of calculating Reduced Level (RL): 2) Line of collimation method (Height of instrument method): In this method the elevation of the line of collimation for every set up of the instrument is found out and the reduced levels of different points with reference to the line of collimation are obtained,In this method the accuracy of the work can be checked by applying the following rule. ‘The difference of the sum of fore and back readings is equal to the difference of the R.L. of first point and the last point. i.e. EFore readings - YBack readings = First R-L. — Last R.L. b) Rise and Fall method: ¥ In this method if the staff reading at a point is greater than the preceding one, it indicates a fall (-Ve) and staff reading at a point is smaller than the preceding one, it indicates a rise (+ve). The accuracy of the work can be checked by applying the following rule: yBack readings - Fore readings = Total rise - Total fall = Last RL. ~ First RL, Example: In a levelling work there are two setup of the instrument at A and B. From the position ‘A staff readings on P, Py, P2, Ps, Ps and C, are 5.42, 7.24, 6.46, 5.38, 6.55 and 6.92 ft respectively. From position B staff readings on Cp, Ps, Ps, Ps, Ps and Ps are 8,78, 8.52, 6.24, 5.96, 6.35 and 7.54 ft respectively. If the R.L. of the bench mark P is 100.00’, calculate the reduced level of the above points by both the methods and apply necessary checks. Solution: a) Line of collimation method: Station | Distance | Staff reading Height of | Reduced | Remark Back | Inter [Fore __| instrument | level A__|o 5.42 105.42 | 100.00 __| Bench mark 50 7.24 98.18 100 6.46 98.96 150. 5.38 100.04 200 6.55 98.87 B 250 8.78 6.92 107.28 98.50, Change point 300 8.52 98.76 350 6.24 101.04 400 5.96 101.32 450 6.35 100.93 500 7.54 99.74 Sum 14.20 14.46 *Height of instrament at B = (Back reading — Fore reading) + Height of instrument at A Check: Sum of fore readings ~ Sum of back readings = 14.46 — 14.20 = 0.26 fi. First R.L. — Last RL. = 100.00 ~ 99.74 = 0.26 ft. b)_Rise and Fall method: Station | Distance | Staff reading Difference. Reduced | Remark x 5 Be Inter Fore Rise Fall level 50 7.24 1,82 ae pectin 100 6.46 0.78 98.96 150 5.38 1.08 100.04 z 208 ci 6.55 117 98.87 250 % a 692 0.37 | 98.50 | Change point x 0.26 98.76 358 oa 2.28 101.04 7 338 0.28 101,32 500 ~ [isa Lis [oon Sum 14.20 14.46 [4.68 4.94 anFall at 50 ft. distance = 5. Rise at 300 ft. distance = 8.78 - 8.52 Sum of back readings — Sum of fore readings = 14.46 — 14.20 = 0.26 Total rise - Total fall = 4.94 - 4.68 = 0.26 Last R.L. — First R.L. = 100.00 - 99.74 = 0.26 Check: f Curvature on Levelling: . | — cre of curvature on levelling is to increase the staff reading because the line of collimation i i i II survey works this effect is not generally is not a level line but a horizontal one. For ordinary smal v fe r ensidered but for precise levelling and longer sights, correction for curvature is to be anplie. As the distance AB increases, the difference BC, between the level line and the collimation line goes on increasing. kK | —Hp Inu From figure, (OB)? = (OA)? + (AB? => (OC + CB) = (OA)? + (AB)? (for small distance AC = AB) => (OC)? + 2xOCxCB + (CB)? = (OA)? + (AB)? => R2+2Rxh+h?=R2+P => hQR+h)=/? PP (nis very small in comparison to 2R) sha == 2R+h 2K 2 =h -4. where D is the diameter of the earth = 7916 miles 2 ‘im nil 1* x5280_ 2,2 ‘ When / is in miles, h= ————— (approximatel 7916 3 om ”) So the error due to curvature is in ft. is equal to two-third of the square of the distance in miles. This is approximately 8 inches for first mile. ‘Thus the correct staff reading = Observed staff reading - 22 Effect of refraction on Levelling: In case of the effect of curvature it is assumed that the rays of light follow a horizontal line (path) from the staff. This correction should be added to the staff reading, It is generally taken as 1/7" of the correction due to curvature. So correction due to curvature =}. 2 2 = 2 ;2 PS) a -.Correct staff reading = Observed staff reading — correction due to curvature + correction due to refraction a 12 = Observed staff reading ~£1? +3? = Observed staff reading 4 (where /is in mile)pramples A dumpy level was placed at C on a line AB, 2200 ft from A and 4500 ft from B. The pack reading on A is 4,98 ft and the fore reading on B is 12.76 ft. calculate the true difference of jovel between A and B. Corrected staff reading on A = Observed staff reading -4 2 4(2200 =498 -2[2°°) = (ze) 4.88 ft Corrected staff reading on A 2 = 12.76 (3) = 12.348 7\ 5280, Difference of level between A and B = 12.34 — 4,88 = 7.46 ft A c | 2200" ol sao —f Example: The top of the Kutubdia light house is visible just above the horizon from a certain place in the Bay of Bengal. The distance of the light house from the observer is 20 miles. Calculate the height of the light house. f— 20mile —+ Let the height of the light house is / ft. Tr — 42 Ap? h=z =—(20) h si =7(20) - 4 = 228.5 ft Example: In the above problem if the height of the observer is 50 ft from the sea level. What is the height of the light house? Let hy = height of the light house hy = height of the light house = 50 ft Here, meth? t=4 ere, 471 2 and 1=1+h=20 We get, I = | thy = 480 =9.35 miles and 1) =20-9.35 = 10.65 miles So height of the light house /y hy $x(1065)? = 64.81 2.