checking the leveling work in surveying

 BUILDING SITE SURVEY AND SET OUT

Carrying out a level traverse

To determine the difference in level between points on the surface of the ground a 'series' of levels will need to be carried out; this is called a level traverse or level run.

Leveling or Field Procedures

The leveling or field procedure that should be followed is shown in Figure 1 below..

Procedure:

1. Set up the leveling instrument at Level position 1.
2. Hold the staff on the Datum (RL+50 m) and take a reading. This will be a backsight, because it is the first staff reading after the leveling instrument has been set up.
3. Move the staff to A and take a reading. This will be an intermediate sight.
4. Move the staff to B and take a reading. This also will be an intermediate sight.
5. Move the staff to C and take a reading. This will be another intermediate sight.
6. Move the staff to D and take a reading. This will be a foresight; because after this reading the level will be moved. (A changeplate should be placed on the ground to maintain the same level.)
7. The distance between the stations should be measured and recorded in the fieldbook (see Table 1)
8. Set up the level at Level position 2 and leave the staff at D on the changeplate. Turn the staff so that it faces the level and take a reading. This will be a backsight.
9. Move the staff to E and take a reading. This will be an intermediate sight.
10. Move the staff to F and take a reading. This will be a foresight; because after taking this reading the level will be moved.
11. Now move the level to Leveling position 3 and leave the staff at F on the changeplate.

Now repeat the steps describe 8 to 10 until you finished at point J.

Field procedures for leveling

All staff readings should be recorded in the fieldbook. To eliminate errors resulting from any line of sight (or collimation) backsights and foresights should be equal in distance. Length of sight should be kept less than 100 metres. Always commence and finish a level run on a known datum or benchmark and close the level traverse; this enables the level run to be checked.

Booking levels

There are two main methods of booking levels:

• rise and fall method
• height of collimation method

Table 1   Rise & Fall Method

Back- sight	Inter- mediate	Fore- sight	Rise	Fall	Reduced level	Distance	Remarks
2.554					50.00	0	Datum RL+50 m
	1.783		0.771		50.771	14.990	A
	0.926		0.857		51.628	29.105	B
	1.963			1.037	50591	48.490	C
1.305		3.587		1.624	48.967	63.540	D / change point 1
	1.432			0.127	48.840	87.665	E
3.250		0.573	0.859		49.699	102.050	F / change point 2
	1.925		1.325		51.024	113.285	G
3.015		0.496	1.429		52.453	128.345	H / change point 3
		0.780	2.235		54.688	150.460	J
10.124		5.436	7.476	2.788	54.688		Sum of B-sight & F-sight, Sum of Rise & Fall
-5.436			-2.788		-50.000		Take smaller from greater
4.688			4.688		4.688		Difference should be equal

The millimeter reading may be taken by estimation to an accuracy of 0.005 metres or even less.

1. Backsight, intermediate sight and forsight readings are entered in the appropriate columns on different lines. However, as shown in the table above backsights and foresights are place on the same line if you change the level instrument.
2. The first reduced level is the height of the datum, benchmark or R.L.
3. If an intermediate sight or foresight is smaller than the immediately preceding staff reading then the difference between the two readings is place in the rise column.
4. If an intermediate sight or foresight is larger than the immediately preceding staff reading then the difference between the two readings is place in the fall column.
5. A rise is added to the preceding reduced level (RL) and a fall is subtracted from the preceding RL

Arithmetic checks

While all arithmetic calculations can be checked there is no assurance that errors in the field procedure will be picked up. The arithmetic check poves only that the rise and fall is correctly recorded in the approriate rise & fall columns. To check the field procedure for errors the level traverse must be closed. It is prudent to let another student check your reading to avoid a repetition of the level run.

If the arithmetic calculation are correct, the the difference between the sum of the backsights and the sum of the foresights will equal:

• the difference between the sum of the rises and the sum of the falls, and
  
  
• the difference between the first and the final R.L. or vice versa.
  (there are no arithmetic checks made on the intermediate sight calculations. Make sure you read them carefully)

Table 2  Height of collimation method (height of instrument)

Back- sight	Inter- mediate	Fore- sight	Height of collimation	Reduced level	Distance	Remarks
2.554			52.554	50.00	0	Datum RL+50 m
	1.783			50.771	14.990	A
	0.926			51.628	29.105	B
	1.963			50591	48.490	C
1.305		3.587	50.272	48.967	63.540	D / change point 1
	1.432			48.840	87.665	E
3.250		0.573	52.949	49.699	102.050	F / change point 2
	1.925			51.024	113.285	G
3.015		0.496	55.468	52.453	128.345	H / change point 3
		0.780		54.688	150.460	J
10.124		5.436		54.688		Sum of B-sight & F-sight, Difference between RL's
-5.436				-50.000		Take smaller from greater
4.688				4.688		Difference should be equal

1. Booking is the same as the rise and fall method for back-, intermediate- and foresights. There are no rise or fall columns, but instead a height of collimation column.
2. The first backsight reading (staff on datum, benchmark or RL) is added to the first RL giving the height of collimation.
3. The next staff reading is entered in the appropriate column but on a new line. The RL for the station is found by subtracting the staff reading from the height of collimation
4. The height of collimation changes only when the level is moved to a new position. The new height of collimation is found by adding the backsight to the RL at the change point.
5. Please note there is no check on the accuracy of intermediate RL's and errors could go undetected.

The rise and fall method may take a bit longer to complete, but a check on entries in all columns is carried out. The RL's are easier to calculate with the height of collimation method, but errors of intermediate RL's can go undetected. For this reason students should use the rise and fall method for all leveling exercises.

Closed and open traverse

Always commence and finish a level run on a datum, benchmark or known RL. This is what is known as a closed level traverse, and will enable you to check the level run.

Closed level traverse
Series of level runs from a known Datum or RL to a known Datum or RL.
Misclosure in millimeter
  24 x √km

Closed loop level traverse
Series of level runs from a known Datum or RL back to the known Datum or RL.
Misclosure in millimeter
  24 x √km

Open level traverse
Series of level runs from a known Datum or RL. This must be avoided because there are no checks on misreading

Areas

Area calculations refer usually to rectangular and triangular shapes. If you need the trigonometric function for calculations click here.

There are different ways to calculate the area of the opposite figure. Try to minimise the amount of calculation. The figure could be divided in three distinct areas
a=10.31x5.63+
b=6.25x5.76+
c=10.39x4.79
or the whole rectangle minus the hole (d)
A =16.67x10.31-6.25x4.55.

As you can see the 2nd method is easier. Look at the shape and try to shorten the calculations.

If you know only the sides of a triangle then use the formula given in the figure below.

An area can usually be divided it in triangles (rectangles, parallelograms, trapeziums etc).

Parallelograms has opposite sides parallel and equal. Diagonals bisect the figure and opposite angles are equal..

 

The trapezium has one pair of opposite sides parallel.
(A regular trapezium is symmetrical about the perpendicular bisector of the parallel sides.)

 

An arc is a part of the circumference of a circle; a part proportional to the central angle.
If 360° corresponds to the full circumference. i.e. 2  r then for a central angle of  (see opposite figure) the corresponding arc length will be b = /180 x r .

Volumes

Volume calculations for rectangular prism and pyramid are shown below:

A truncated pyramid is a pyramid which top has been cut off.

If the A₁+A₂ is almost equal in size then the following formula can be used instead:

V = h × (A₁ + A₂) / 2

A prismoid is as a solid whose end faces lie in parallel planes and consist of any two polygons, not necessarily of the same number of sides as shown opposite, the longitudinal faces may take the form of triangles, parallelograms, or trapeziums.