LEVELLING IN SURVEYING

LEVELLING IN SURVEYING

Leveling is an operation in surveying performed to determine the difference in levels of two points. By this operation the height of a point from a datum, known as elevation, is determined.

LEVEL SURFACE

A level surface is the equipotential surface of the earth’s gravity field. It is a curved surface and

every element of which is normal to the plumb line.

DATUM

A datum is a reference surface of constant potential, called as a level surface of the earth’s gravity field, for measuring the elevations of the points. One of such surfaces is the mean sea level surface and is considered as a standard datum. Also an arbitrary surface may be adopted as a datum.

LEVEL LINE

A line lying in a level surface is a level line. It is thus a curved line.

A level in proper adjustment, and correctly set up, produces a horizontal line of sight which

is at right angles to the direction of gravity and tangential to the level line at the instrument height. It follows a constant height above mean sea level and hence is a curved line, as shown in Fig. 3.1. Over short distances, such as those met in civil engineering works, the two lines can be taken to coincide. Over long distances a correction is required to reduce the staff readings given by the horizontal line of sight to the level line equivalent. Refraction of the line of sight is also to be taken into account. The corrections for the curvature of the level line Cc and refraction Cr are shown in

 

DIRECT DIFFERENTIAL OR SPIRIT LEVELLING

Differential leveling or spirit leveling is the most accurate simple direct method of determining the difference of level between two points using an instrument known as level with a leveling staff.

A level establishes a horizontal line of sight and the difference in the level of the line of sight and

the point over which the levelling staff is held, is measured through the levelling staff. Fig. 3.3 shows the principle of determining the difference in level Äh between two points A and B, and thus the elevation of one of them can be determined if the elevation of the other one is known. SA and SB are the staff readings at A and B, respectively, and hA and hB are their respective elevations.

From the figure, we find that

(i) if SB < SA, the point B is higher than point A.

(ii) if SB > SA, the point B is lower than point A.

(iii) to determine the difference of level, the elevation of ground point at which the level is

set up, is not required.

Booking and Reducing the Levels

Before discussing the booking and methods of reducing levels, the following terms associated with differential leveling must be understood.

Station: A station is the point where the leveling staff is held. (Points A, a, b, B, c, and C

in Fig. 3.4).

Height of instrument (H.I.) or height of collimation: For any set up of the level, the

elevation of the line of sight is the height of instrument. (H.I. = hA + SA in Fig. 3.3).

Back sight (B.S.): It is the first reading taken on the staff after setting up the level usually

to determine the height of instrument. It is usually made to some form of a bench mark (B.M.) or

to the points whose elevations have already been determined. When the instrument position has to be changed, the first sight taken in the next section is also a back sight. (Staff readings S1 and S5

 

 

Fore sight (F.S.): It is the last reading from an instrument position on to a staff held at a point.

It is thus the last reading taken within a section of levels before shifting the instrument to the next

section, and also the last reading taken over the whole series of levels. (Staff readings S4 and S7

in Fig. 3.4).

Change point (C.P.) or turning point: A change point or turning point is the point where

both the fore sight and back sight are made on a staff held at that point. A change point is required before moving the level from one section to another section. By taking the fore sight the elevation of the change point is determined and by taking the back sight the height of instrument is determined.

The change points relate the various sections by making fore sight and back sight at the same point. (Point B in Fig. 3.4).

Intermediate sight (I.S.): The term ‘intermediate sight’ covers all sightings and consequent

staff readings made between back sight and fore sight within each section. Thus, intermediate sight station is neither the change point nor the last point. (Points a, b, and c in Fig. 3.4).

Balancing of sights: When the distances of the stations where back sight and fore sight are

taken from the instrument station, are kept approximately equal, it is known as balancing of sights. Balancing of sights minimizes the effect of instrumental and other errors.

Reduced level (R.L.): Reduced level of a point is its height or depth above or below the

assumed datum. It is the elevation of the point.

 

Rise and fall: The difference of level between two consecutive points indicates a rise or a

fall between the two points. In Fig. 3.3, if (SA – SB) is positive, it is a rise and if negative, it is

a fall. Rise and fall are determined for the points lying within a section.

Section: A section comprises of one back sight, one fore sight and all the intermediate sights

taken from one instrument set up within that section. Thus the number of sections is equal to the

number of set ups of the instrument. (From A to B for instrument position 1 is section-1 and from

B to C for instrument position 2 is section-2 in Fig. 3.4). For booking and reducing the levels of points, there are two systems, namely the height of instrument or height of collimation method and rise and fall method. The columns for booking the readings in a level book are same for both  the methods but for reducing the levels, the number of additional columns depends upon the method of reducing the levels.

Note that except for the change point, each staff reading is written on a separate line so that each staff position has its unique reduced level. This remains true at the change point since the staff does not move and the back sight from a forward instrument station is taken at the same staff position where the fore sight has been taken from the backward instrument station.

To explain the booking and reducing levels, the levelling operation from stations A to C shown in Fig. 3.4, has been presented in Tables 3.1 and 3.2 for both the methods. These tables may have additional columns for showing chainage, embankment, cutting, etc., if required

 

In reducing the levels for various points by the height of instrument method, the height of

instrument (H.I.) for the each section highlighted by different shades, is determined by adding the elevation of the point to the back sight reading taken at that point. The H.I. remains unchanged for all the staff readings taken within that section and therefore, the levels of all the points lying in that section are reduced by subtracting the corresponding staff readings, i.e., I.S. or F.S., from the H.I. of that section.

In the rise and fall method, the rises and the falls are found out for the points lying within

each section. Adding or subtracting the rise or fall to or from the reduced level of the backward

 

The arithmetic involved in reduction of the levels is used as check on the computations. The

following rules are used in the two methods of reduction of levels.

(a) For the height of instrument method

(i) Ó B.S. – Ó F.S. = Last R.L. – First R.L.

(ii) Ó [H.I. . (No. of I.S.’s + 1)] – Ó I.S. – Ó F.S. = Ó R.L. – First R.L.

(b) For the rise and fall method

Ó B.S. – Ó F.S. = Ó Rise – Ó Fall = Last R.L. – First R.

COMPARISON OF METHODS AND THEIR USES

Less arithmetic is involved in the reduction of levels with the height of instrument method than with the rise and fall method, in particular when large numbers of intermediate sights is involved. Moreover, the rise and fall method gives an arithmetic check on all the levels reduced, i.e., including the points where the intermediate sights have been taken, whereas in the height of instrument method, the check is on the levels reduced at the change points only. In the height of instrument method the check on all the sights is available only using the second formula that is not as simple as the first one.

The height of instrument method involves less computation in reducing the levels when there

are large numbers of intermediate sights and thus it is faster than the rise and fall method.

The rise and fall method, therefore, should be employed only when a very few or no intermediate sights are taken in the whole leveling operation. In such case, frequent change of instrument position requires determination of the height of instrument for the each setting of the instrument and, therefore, computations involved in the height of instrument method may be more or less equal to that required in the rise and fall method. On the other hand, it has a disadvantage of not having check on the intermediate sights, if any, unless the second check is applied.