DEFINITIONS, PRINCIPLES AND CHAIN SURVEYING

Fundamentals surveying

1. OVERVIEW OF SURVEYING Lecture 1: Definition, Principles, Types & Classification By B. KAMAL, Assistant Professor 20CE204 & GEODESY

2. Surveying Those activities involved in planning and execution of surveys for the Location, Design, Construction, Operation and Maintenance of Civil and Other Engineering Projects.” 2

3. SURVEYING - Definition Surveying is the art and science of determining the relative positions of various points or stations on the surface of the earth by measuring the horizontal and vertical distances , Angles and taking the details of these points and by preparing a map or plan to any scale. Measurements taken in Horizontal and Vertical planes. 3 Measurements taken in Horizontal and Vertical planes.

4. Objectives of Surveying 4

5. Uses of Surveying To   prepare a Topographical Map which shows hills, valleys, river, forests, villages, towns etc. To prepare a Cadastral Map which shows the boundaries of fields, plots houses and other properties. To prepare an Engineering Map which shows the properties of engineering works such as buildings, roads, railways , dams, canals, etc. To prepare a Contour Map to know the topography of the area to find out the best possible site for road , railways, bridges, reservoirs , canals, etc. To prepare Military Maps, Geological Maps, Archeological Maps etc. To set out works and transfer details from the work on the ground. 5

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13. Primary Divisions of Surveying Type of surveying in which earth surface is considered as a plane and the curvature of the earth is ignored. In such surveying the line joining any two stations is considered to be straight. 13 Plane surveying Geodetic surveying Type of surveying in which the curvature of the earth is taken into consideration. The line joining any two stations is considered as curved line.

14. Difference Between Geodetic and Plane Surveying Earth surface is considered as a plane surface. The curvature of the earth is ignored. The line joining any two stations is considered as a straight line. The triangle formed by any three points is considered as a plane. The angles of the triangle are considered to be plane angles. Carried out for a small area < 250km 2 Earth surface is considered as a curved surface. The curvature of the earth is taken into account. The line joining any two stations is considered as a curved line. The triangle formed by any three points is considered as spherical. The angles of the triangle are considered to be spherical . Carried out for a large area >250km 2 . 14

15.   Fundamental Principles of Surveying Two basics principles of survey Whole To Part: Always work from whole to part. Locate A Point By at least Two Measurements: Locate a new station by at least two measurements whether linear or angular from fixed reference points. 15

16. Fundamental Principles of Surveying Work from whole to the part: According to the first principle, the whole survey area is first enclosed by main stations (i.e.. Control stations) and main survey lines. The area is then divided into a number of divisions by forming well conditioned triangles. The main survey lines are measured very accurately with precise survey instruments. The remaining sides of the triangle are measured. The purpose of this method of working is to control accumulation of errors. During measurement, if there is any error, then it will not affect the whole work, but if the reverse process is followed then the minor error in measurement will be magnified. 16

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18. Fundamental Principles of Surveying To locate a new station by at least two measurements ( Linear or angular) from fixed reference points. According to the second principle the points are located by linear or angular measurement or by both in surveying. If two control points are established first, then a new station can be located by linear measurement. Let A & B are control points, a new point C can be established. Following are the methods of locating point C from such reference points A & B. The distance AB can be measured accurately and the relative positions of the point can be then plotted on the sheet to some scale. 18

19. Fundamental Principles of Surveying Taking linear measurement from A and B for C. Taking linear measurement of perpendicular from D to C. Taking one linear measurement from B and one angular measurement as∕ ABC Taking two angular measurement at A & B as angles ∟CAB and ∟ ABC. Taking one angle at B as ∟ABC and one linear measurement from A as AC. 19

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21. Classification of Surveying 21

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23. Based on instruments used 23

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28. Leveling

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36. Geological survey In this both surface and subsurface surveying are conducted to locate different minerals and rocks. In addition, geological features of the terrain such as folds and faults are located. 42

37. Mine Survey Mine survey includes both surface and underground surveys. It is conducted for the exploration of mineral deposits and to guide tunneling and other operations associated with mining 43

38. Archaeological and Military survey Archaeological survey It is conducted to locate relies of antiquity, civilization, kingdoms, forts, temples, etc. Military survey It has a very important and critical applications in the military. Aerial surveys are conducted for this purpose. It is conducted to locate strategic positions for the purpose of army operations. 44

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41. 5. Classification based on methods Triangulation: Triangulation is basic method of surveying, when the area to be surveyed is large, triangulation is adopted. The entire area is divided into networks of triangles. Traversing A Traversing is circuit of survey lines. It may be open or closed . When the linear measurements are done with a chain and a tape and the directions or horizontal angles are measured with a compass or a theodolite respectively the survey is called traversing. 47

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44. Plan vs Map Plan Map A plan is the graphical representation, to some scale, of features on, rear or below the surface of the earth as projected on horizontal plane. If the scale of the graphical representation on a horizontal plane is small, the plan is called a map. A plan is drawn on a large scale. A map is drawn on a small scale. Scale: 1 cm = 10 m or  < 10 m Scale: 1 cm = 100 m or > 100 m On a pan, generally horizontal dist’s & directions are shown. On a topographic map, vertical dist’s (elevations) are also shown by contour lines. A plan is drawn for small area. e.g. – Plan of house, plan of bridge A map is drawn for large area. e.g. – Map of Area 50

45. Linear Measurements – Chain Surveying The primary instrument or equipment used in chain surveying is a chain or a tape. A survey chain is commonly composed of 100 or 150 links formed through pieces of galvanised mild steel wire of 4 mm diameter. The ends of every link are looped and connected together through means of three circular or oval shaped wire rings to gives flexibility to chain. The length of each link is measured as the distance among the centres of two consecutive middle rings. The joints of links are welded to prevent length changes because of stretching. The ends of chain are provided with brass handles with swivel joints. 51

46. This helps in turning the chain without twisting. The end link length includes the length of handle and is measured from the outside of the handle, which is considered as zero point or the chain end. Tallies, which are metallic tags of different patterns, are provided at suitably specified points in the chain to facilitate quick and easy reading. A semi-circular grove is provided in the centre on the outer periphery of handle of chain for fixing the mild steel arrow at the end of one chain length. The number of links in a chain could be 100 in a 20 m chain and 150 in a 30 m chain . 52 Chains

47. Parts of Chains 53

48. Types of chains Metric Chain Metric chains are made in lengths 20m (100 Links) and 30m (150 links). Tallies are fixed at every five-meter length and brass rings are provided at every meter length except where tallies are attached. Surveyor’s Chain or Gunter’s Chain Length = 66’ (22 yards), No of links = 100, Each link = .66’ Used for measuring distances in miles or furlongs (220 yards), acres (Area). Engineer’s Chain Length = 100’, No of links = 100, Each link = 1’ Used in all  Engineering Surveys . 54

49. Tapes Tapes can be used for more accurate measurements of lengths. They are lighter and easier to handle and comparatively less liable to change in length than chain. Depending on the material, these can be of following types : (a) Cloth or linen tape (b) Metallic tape (c) Steel tape or Steel band (d) Invar tape 55

50. Cloth or linen tapes are 12 to 15 mm wide closely woven linen varnished for moisture proofing. Commonly used lengths are 10 m, 20 m, and 30 m. Since these are liable to shrink when wet and alter in length due to twisting or stretching, these are rarely used for accurate measurements . For accurate measurements, steel tapes are used. These consist of light strip of steel with width ranging from 6 to 10 mm, in lengths of 2 to 50 m. Alternatively, steel bands consisting of ribbon of steel with brass swivel handle at each end are used. The width is usually 16 mm and length of 20 or 30 m. Invar tapes of alloy of Nickel (36%) and steel can be used for higher accuracy as their coefficient of thermal expansion is very low. However, it is costly and more delicate in use. In recent times, fibre glass tapes are extensively used in the field survey because of its low thermal expansion, cheapness, strength, ruggedness and durability. These are available in ranges varying from 5 m to 30 m in length. 56

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52. Other Auxiliary Equipment Arrows Arrows or chain pins and made of stout steel wire 4 mm in diameter, 400 to 450 mm long and black enameled. These are used to mark the end of each chain length. 58

53. Other Auxiliary Equipment Wooden Pegs These are made of stout timber generally 25 to 30 mm square or circular size and 150 mm long as shown in Figure. Wooden pegs are normally used to mark station position on ground on a quasi-permanent state. These are tapered at one end so that they can be driven in the groundwith a hammer. These are kept at about 40 mm (minimum) projecting above the ground. 59

54. Other Auxiliary Equipment Wooden Pegs These are octagonal or circular in plan normally 25 to 30 mm diameter straight timber or tubular steel rods, 3 m in length and provided with an iron shoe at lower end as shown in Figure 2.2(c). These are painted in black and white alternate bands and normally have a flag at the top for easy recognition and identification from a distance. If the ranging roads are graduated in meters and one tenth of a meter, they are called offset rods and are used for measurement of short offsets. 60

55. Other Auxiliary Equipment Ranging Rods These are octagonal or circular in plan normally 25 to 30 mm diameter straight timber or tubular steel rods, 3 m in length and provided with an iron shoe at lower end as shown in Figure. These are painted in black and white alternate bands and normally have a flag at the top for easy recognition and identification from a distance. If the ranging roads are graduated in meters and one tenth of a meter, they are called offset rods and are used for measurement of short offsets. 61

56. Other Auxiliary Equipment 62

57. Other Auxiliary Equipment Plumb Bob It is usually heavy spherical or conical ball, as shown in Figure, of metal and is used to transfer points on ground by suspending it with the help of a strong thread. It is used in measuring distances on sloping ground by stepping. Compass, Dumpy levels and Theodolites are also positioned over the station point accurately with the help of plumb bobs. 63

58. Other Auxiliary Equipment Line ranger A line ranger consists of either two plane mirrors or two right angled isosceles prisms placed one above the other as depicted in Figure. The diagonals of both the prisms are silvered so as to reflect the incident rays. Line rangers are provided with a handle to hold the instrument. A line ranger can also be used to draw offset on a chain line. 64

59. Other Auxiliary Equipment – Cross staff Establishing perpendicular offset from a given point to a line and Setting out a right angle at a given point on a line There are two forms of cross staff commonly used namely a. Open cross staff b. French cross staff 65

60. Other Auxiliary Equipment OPEN CROSS STAFF simplest form of cross staff is open cross staff shown in figure. It consists of two pairs of vertical slits providing two lines of sight mutually at right angles. Each pair consists of 2 vanes, one is eye vane and other is objective vane. 66

61. French cross staff It  consists of an octagonal brass tube with slits on all eight sides. on the other sides there are vertical slits, which are at 45 degrees to those previously mentioned, for setting out angles of 45 degrees. The base carries a brass socket so that it may be fitted on the pointed staff when the instrument is to be used. 67 Other Auxiliary Equipment

62. We l l conditi o n e d trian gle, ill conditi o n e d tri a ngle and ideal tri a ngle . A triang l e i s sa i d t o b e w e l l c o n d i ti o n ed tri a ngle w hen no a n gle i n i t i s n e it h er less than 3 no r g r e a t er than 120 . If in a triangle an angle is less than 30 or 120 is called ill conditioned triangle. An equilateral triangle having each angle of 60 is an ideal triangle. 68

63. Errors in Chaining Any field surveying including chain surveying is fraught with many errors including observational errors, affecting the accuracies of measurements and mapping. It is essential to identify, rectify and adjust these errors before the results of surveying can be used for any engineering applications. The errors can be broadly classified as (a) Instrumental errors - caused by imperfections in instruments, wear and tear of instruments due to continuous use and their rough handling. (b) Observational errors - introduced because of involvement of human factor in surveying process. 69

64. Gross Errors Gross errors or mistakes are blunders that occur due to inexperience or carelessness on the part of the surveyor. In chain surveying, these could be due to displacement or loss of pegs or arrows, provided to identify and fix the location of various types of stations and other places of interest, reading the chain or tape in a wrong manner or using an instrument in an incorrect way, and wrong recoding of measurements in the record book, e.g. field book. 70

65. Systematic errors Systematic errors follow some specific pattern according to some mathematical or physical law. In the context of chain surveying, these could be due to erroneous length of chain or tape (+ve or –ve), erroneous ranging, links in chain not straight (local bends) due to rough handling or twisting of metallic tapes, etc., non-horizontally of chain/tape over rough ground terrain, sag in chain or tape, when it is stretched across a depression in ground, variation in temperature and/or dampness, and variation in pull applied during measurement. 71

66. Corrections Correction for Erroneous Length of Chain/Tape True or Correct Distance = L′/ L× Measured Distance where, L′ = Actual incorrect length of chain, and L = Designated length of chain. Correction for Temperature Correction (C t ) is given by C t = α (T m – T o )L where, α = Coefficient of thermal expansion, T m = Mean temperature in the field during measurement, T = Standard temperature for the tape, and L = Measured distance. 72

67. Corrections Correction for Pull C P = ( P- P o /AE) L where, P = Pull applied during measurements (kg or N), P = Standard pull, L = Measured length, A = Cross-sectional area of the tape (cm2 or mm2), and E = Young’s modulus of elasticity (kg/cm2 or N/mm2). Correction for sag If length measured ‘L’ and the difference in the levels of first and last point ‘h’ are given then correction for slope is, C=h 2 /2L If θ and L are given, C=L (1-cosθ) This correction is always subtractive. 73

68. Corrections Correction for Sag While taking reading, if the tape/Chain is suspended between two supports, the tape/chain sags under its own weight. Hence, measured length is more than the actual length. Hence, this correction is subtractive. This correction is given by C s = LW 2 / 24 P 2 C s = Chain correction per length L= Total length of chain/tape W= Total weight of the chain/ tape P= Pull applied 74

69. Random or Accidental errors Random or Accidental errors can occur due to lack of perfection of human eye and or human behaviour. Even the best and efficient surveyor can have fatigue effect after working for long duration in strenuous environment causing observational errors. Using suitable probability distribution functions, these errors can then be adjusted, distributed among various measurements and accounted for. Each surveying method or process can be assigned a reliability factor (or risk factor) for accuracy depending on the analysis of probability behaviour. 75

70. Problem 1 - A 30 m chain was found to be 3 cm too long after chaining 1800 m. The same chain was observed to be 5 cm too long after chaining the total distance of 3600 m. Assuming that the chain was correct at the commencement of work, find the true length of the total distance chained. Solution (a) During chaining from 0 m to 1800 m: Initial length of chain at commencement of work = 30.0 m Final length of chain at end of chaining up to 1800 = 30.03 m Average true length of chain during this exercise 30.03 +30.00/2 = 30.015 m True distance of measured distance 1800 m = L′ /L× 1800 30.015/ 30.00 x1800 = 1800.90 m 76

71. (b) During measurements from 1800 to 3600 m: Initial length of chain = 30.03 m Final length of chain = 30.05 m Average true length of chain during this measurement (30.03 +30.05)/2 = 30.04 m Measured distance = 3600 – 1800 = 1800 m True measured distance (30.04/30.00)* 1800 =1802.40 m Total true distance chained = 1800.90 + 1802.40 = 3603.30 m. 77

72. Problem 2 - A chain was calibrated to be of exact length 30.00 m at 20 o C. When this chain was used for chain surveying in field, the temperature was recorded to be 45 o C. If the coefficient of linear expansion of steel used in chain is 8 × 10 – 6 per o C, find the true total distance chained if measured distance on ground is 6000 m. Solution True length of chain at 20 o C = 30.00 m True length of chain at 45 o C would be L = L (1 + α t) = 30.00 [1 + (8 × 10 -6 ) × (45 – 20)] = 30.00 × (1 + 0.0002) = 30.06 m True measure distance 30.06/30.0×6000 = 6012 m. 78

73. Problem 2 - A chain was calibrated to be of exact length 30.00 m at 20 o C. When this chain was used for chain surveying in field, the temperature was recorded to be 45 o C. If the coefficient of linear expansion of steel used in chain is 8 × 10 – 6 per o C, find the true total distance chained if measured distance on ground is 6000 m. Solution True length of chain at 20 o C = 30.00 m True length of chain at 45 o C would be L = L (1 + α t) = 30.00 [1 + (8 × 10 -6 ) × (45 – 20)] = 30.00 × (1 + 0.0002) = 30.06 m True measure distance 6000 00 .3006 .30× = 6012 m. 79

74. Problem 3 - A survey line AB was measured by a chain of 30 m length and was found to be 2340 m. The same line AB when measured by a 20 m chain, the length was recorded as 2350 m. While calibrating the 30 m chain was found to be 2 cm too short. What was the error in 20 m chain? Solution Actual length of 30 m chain = 30.0 – 0.02 = 29.98 m True length of AB = L′ /L× Measured Length = (29.98/30.00) * 2340 = 2338.44 m When AB was measured by 20 m chain. True length = L′ /L × Measured Length 2338.44 = L′ / 20 × 2350 L ′ = 2338.44*20/ 2350 = 19.902 m ≈ 19.90 m Hence, the incorrect actual length of 20 m chain is 19.90 m, i.e. 10 cm too short. 80

75. Problem 4 - A sloping ground with a gradient of 1 in 10 was surveyed with a 30 m chain. The chain was checked at commencement of work, at mid station C of survey line AB and at the end of survey and was found to be 2 cm, 6 cm and 10 cm too long respectively. If the measured length of survey line AB = 6000 m, find the true length of AB. Solution Actual length of 30 m chain at A = 30.02 m Actual length of 30 m chain at C = 30.06 m Average length of chain during measurement from A to C (30.02 +30.06) /2 = 30.04 m Actual length of AC measured along slope = (30.04/ 30.0) *3000 = 3004 m Actual chain length at C = 30.06 m Actual chain length at B = 30.10 m Average length of chain during measurement from C to B 81

76. Problem 4 - A sloping ground with a gradient of 1 in 10 was surveyed with a 30 m chain. The chain was checked at commencement of work, at mid station C of survey line AB and at the end of survey and was found to be 2 cm, 6 cm and 10 cm too long respectively. If the measured length of survey line AB = 6000 m, find the true length of AB. Solution Actual length of 30 m chain at A = 30.02 m Actual length of 30 m chain at C = 30.06 m Average length of chain during measurement from A to C (30.02 +30.06) /2 = 30.04 m Actual length of AC measured along slope = (30.04/ 30.0) *3000 = 3004 m Actual chain length at C = 30.06 m Actual chain length at B = 30.10 m Average length of chain during measurement from C to B 82

77. ( 30.06 +30.10)/2 =30.08 m Actual length of CB measured along slope (30.08/ 30.0)*3000 =3008 m Actual length of line AB along slope = 3004 + 3008 = 6012 m A slope of ground is 1 in 10, i.e. 1 m vertical in 10 m horizontal, e.g. EF = 1 m and DE = 10 m. Then DF along slope = √10 2 +1 2 = 10.05 Thus, when sloping length is 10.05 m, horizontal length is 10.00 m. Hence, true horizontal distance between AB would be 10.00/ 10.05 *6012 m = 5985.07 m 83

78. Problem 5 - A 50 m tape is suspended between the ends under a pull of  150 N.  The mass of the tape is 1.52 kilograms.  Find the corrected length of the tape. Solution             Cs = LW 2 / 24 P2 Correction for sag  = Cs = l 1  (mg) 2  / 24 P 2                  l1 = 50 m; M = 1.52 kilograms; P = 150 N.             ~ Cs = 50 x (1.52 x 9.81) 2  / 24 x 150 2  = 0.0206 m.             ~ Corrected length of the tape   = l – C s                                                                = 50 – 0.0206                                                                 = 49.9794 m. 84

79. Obstacles in Chain Surveying (a) obstacles in ranging, (b) obstacles in chaining (measuring horizontal distance), and (c) obstacles in recording details. 85

80. Obstacles in ranging If the two ends of a survey line A and B are not visible from intermediate point on it, then reciprocal ranging cannot solve the problem. In such cases, a random line AB1 is drawn in any convenient direction but as close to point B as possible (Figure 2.13). The point B1 is chosen such that it is visible from B and BB1 is perpendicular to the random line. Measure BB1, select points C1 and D1 on the random line and erect perpendicular C1C and D1D on it. The value of C1C and D1D can be calculated as B 86 After getting points C and D, join CD and prolong it.

81. Obstacles in chaining total length L between A (A ) and B (A n ) will be L = Σ δl i i = 1 87 Ground with Large Slope

82. Obstacles in chaining 88 Figure 2.15(a) : Object with Curved Boundary