Engineering Surveying -1 CE212 LevellingLectures

Lecture

2016, October 31

Muhammad Noman

Levelling

Definition: The art of determining the relative heights of different points on or below the surface of Earth is known as Levelling.

Objective: The aim of levelling is to determine the relative heights of different objects on or below the surface of the earth and to determine the undulation of the ground surface.

Definitions

1. Level Surface: Any surface parallel to the mean spheroidal surface of the earth is said to be a level surface. Such a surface is obviously curved. The water surface of a still lake is also considered a level surface.

Definitions

02. Level Line: Any line lying on a level surface is called a level line. This line is normal to the plumb line (direction of gravity) at all points.

03. Horizontal Plane: Any plane tangential to the level surface at any point is known as the horizontal plane.

04. Horizontal Line: Any line lying on the horizontal plane is said to be a horizontal line.

Definitions

05. Vertical Line: The direction indicated by a plumb line (the direction of gravity) is known as the vertical line.

06. Vertical Plane: Any plane passing through the vertical line is known as the vertical plane.

07. Datum: This is an imaginary level surface or level line from which the vertical distances of different points (above or below this line) are measured. MSL at Karachi is considered as Datum.

Definitions

08. Reduced Level: The vertical distance of a point above or below the datum line is known as the reduced level of that point. The reduced level may be positive or negative according as the point is above or below the datum.

09. Bench Marks: These are fixed points or marks of known RL determined with reference to the datum line.

Definitions:

There are four types of Benchmarks:

a. GTS Benchmarks: These benchmarks are established by the survey departments at large intervals all over the country. The values of reduced levels, the relevant positions and number of benchmarks are given in catalogue published by this department.

Definitions:

b. Permanent Benchmarks: These are fixed points or marks established by different government departments like PWD, Railways, Irrigation, etc. The RLs of these points are determined with reference to the GTS benchmarks.

Definitions:

c. Arbitrary Benchmarks: When RLs of some fixed points are assumed, they are termed arbitrary benchmarks. They are adopted in small survey operations when only undulation of the ground surface is required to be determined.

d. Temporary Benchmarks: When the benchmarks are established temporarily at the end of a day’s work, they are said to be temporary benchmarks.

Definitions:

10. Back sight Reading (BS): This is the first staff reading taken in any set-up of the instrument after the levelling has been perfectly done. This reading is always taken on a point of known RL, i.e. on a bench-mark or change point.

11. Fore sight reading (FS): It is the last staff reading in any set-up of the instrument, and indicates the sifting of the latter.

Definitions:

12. Intermediate Sight Reading (IS): It is any other staff reading between BS and FS in the same setup of the instrument.

13. Change Point (CP): This point indicates the shifting of the instrument. At this point, a FS is taken from one setting and a BS from next setting.

Types of Levels

The following are the different types of levels:

1. Dumpy level

2. Wye Level (Y-Level)

3. Cooke’s Reversible Level

4. Crushing’s Level

5. Modern Tilting Level

6. Automatic Level

Dumpy level

Wye Level (Y-Level)

Cooke’s Reversible Level

Cushing’s Level

Modern Tilting Level

Automatic level

Types of Levelling Operations

Following are the types of levelling:

1. Simple Levelling

2. Differential Levelling

3. Fly Levelling

4. Longitudinal or Profile Levelling

5. Cross-sectional Levelling

6. Check Levelling

1. Simple Levelling

When difference of level between two points is determined by setting the levelling instrument midway between the points, the process is called simple levelling.

Suppose A and B are two points whose difference of level is to be determined. The level is setup at O, exactly midway between A and B. After proper temporary adjustment, the staff readings on A and B are taken.

2. Differential levelling

The method is adopted to find the difference in elevation between points if:

a. The points are a great distance apart,

b. The difference of elevation between the points is large, and

c. There are obstacles between the points

3. Fly Levelling

When differential levelling is done in order to connect a benchmark to the starting point of the alignment of any project, it is called fly levelling. Fly levelling is also done to connect the BM to any intermediate point of the alignment for checking the accuracy of work. In such levelling, only the back sight and foresight readings are taken at every step-up of the level and no distances are measured along the direction of levelling.

4. Longitudinal or Profile Levelling

The operation of taking levels along the center line of any alignment (road, railway etc.) at regular intervals is known as longitudinal levelling. In this operation, readings are taken at regular intervals at every set-up of the instrument. The operation is taken in order to determine the undulations of the ground surface along the profile line.

5. Cross-Sectional Levelling

The operation of taking levels transverse to the direction of longitudinal levelling, is known as cross-sectional levelling. The cross sections are taken at regular intervals along the alignment. Cross sectional levelling is done in order to know the nature of the ground across the center line of any alignment.

Check Levelling

The fly levelling done at the end of the day’s work to connect the finishing point with the starting point on that particular day is known as check levelling. It is undertaken in order to check the accuracy of the day’s work.

Methods of Levelling

There are two methods for levelling operations

1. Height of Collimation Method

2. Rise and Fall Method

Collimation Method

It consist of finding the elevation of the plane of collimation ( H.I.) for every set up of the instrument, and then obtaining the reduced level of point with reference to the respective plane of collimation.

1. Elevation of plane of collimation for the first set of the level determined by adding back side to R.L. of B.M.

2. The R.L. of intermediate point and first change point are then obtained by starching the staff reading taken on respective point (IS & FS) from the elation of the plane collimation. [H.I.]

Collimation Method

3. When the instrument is shifted to the second position a new plane collimation is set up. The elevation of this plane is obtained by adding B.S. taken on the C.P. From the second position of the level to the R.L. C.P. The R.L. of successive point and second C.P. are found by subtract these staff reading from the elevation of second plane of collimation

Arithmetical check

Sum of B.S. – sum of F.S. = last R.L. – First R.L.

Numerical on Collimation method

1. The following staff reading were taken in succession with a level. The instrument was shifted after 3rd, 6th and 8th reading. By the plane of collimation method, calculate the R.L and all the points. R.L of Bench Mark is 500 meters.

Readings are:

0.365, 1.450, 2.335, 0.855, 2.225, 2.905, 1.275, 0.725, 1.975, 2.305, 2.610, 3.335

Sr. No. B.S I.S F.S P.C R.L Remarks

1 0.365 500.365 500 Bench Mark

2 1.450 498.915

3 2.335 498.030 Change point 1

4 0.855 498.885 498.030

5 2.225 496.660

6 2.905 495.980 Change Point 2

7 1.275 497.255 495.980

8 0.725 496.530 Change point 3

9 1.975 498.505 496.530

10 2.303 496.200

11 2.61 495.895

12 3.355 495.150

Total 4.47 9.32

Check: Sum of B.S – Sum of F.S = Last R.L – First Reduce Level9.32 – 4.47 = 495.150 – 500 = -4.85

2. The following staff reading were taken in succession with a level. The instrument was shifted after 2nd , 4th, 7th and 9th reading. By the plane of collimation method, calculate the R.L and all the points. R.L of Bench Mark is 481.923 meters.

Readings are:

0.422, 0.684, 1.285, 0.506, 1.793, 4.462, 2.416, 3.120, 1.517, 1.234, 1.232

S. No. B.S I.S F.S R.L of P.C R.L Remarks

1 0.422 482.345 481.923 Bench Mark

2 0.684 481.661 Change Point 1

3 1.285 482.946 481.661

4 0.506 482.440 Change Point 2

5 1.793 484.233 482.440

6 4.462 479.771

7 2.416 481.817 Change Point 3

8 3.120 484.937 481.817

9 1.507 483.420 Change Point 4

10 1.234 484.654 483.420

11 1.232 483.422

Total 7.854 6.355

Check: Sum of B.S – Sum of F.S = Last R.L – First Reduce Level7.854 – 6.355 = 483.422 – 481.923 = 1.499

Rise and Fall Method

It consists of determining the difference of elevation between consecutive points by comparing each point after the first that immediately preceding it. The difference between there staff reading indicates a rise fall according to the staff reading at the point. The R.L is then found adding the rise to, or subtracting the fall from the reduced level of preceding point.

Arithmetic check

Sum of B.S. – sum of F. S. = sum of rise – sum of fall = last R. L. – first R.L.

Problem

B.S I.S F.S Rise Fall R.L Remarks

1.5 60.5 Temporary Bench Mark

2.5 1.0 59.5

4.0 1.5 58.0

2.0 2.0 60.0 CP 1

3.0 60.0

5.5 2.5 57.5

1.0 4.5 62.0 CP 2

6.0 62.0

3.0 3.0 65.0

Check = Sum of B.S- Sum of F.S = Sum of Rise- Sum of Fall = Last R.L- First R.L= 10.5 - 6 = 9.5 – 5.5 = 65.0 – 60.5 = 4.5

Differences between height of collimation method and rise and fall method

Assignment # 3

• Q # 1. Reduce the given booking data below using (a) the Rise & Fall and (b) HPC methods. Use arithmetic checks to support your results.

Sr. No. Station B.S I.S F.S R.L

1 1 1.400 50.00

2 1 1.235

3 1 1.870

4 2 1.355

5 2 3.340

6 2 1.975

7 3 0.585

8 3 0.855

Assignment # 3

• Q #2: The data from a survey, are shown below. Use both Rise and Fall method and Height of Plane of Collimation (HPC) method to reduce the data. Use arithmetic checks to support your answer.

Point B.S I.S F.S R.L

TBM 0.771 +43.000

A 0.802 1.552

B 2.311

C 3.580 1.990

D 1.220

E 3.675

F 2.408 4.02

G 0.339

H 0.157