Levelling MCQ Quiz - Objective Question with Answer for Levelling - Download Free PDF

Concept:

Combined correction for curvature and refraction is given by:

C = C_c + C_R

C = - 0.0785 d² + 0.01122 d²

C = - 0.06735 d²

Calculation:

d = 100 m = 0.1 km

C = -0.06735 d²

where d is in km, C is in m

C = - 0.06735 x 0.1² = - 0.000673 m

Concept:

In levelling, when the instrument is shifted between readings, the readings are treated as follows:

• The first reading after setting up the instrument is the Back Sight (BS).

• The last reading before shifting the instrument is the Fore Sight (FS).

• Without a given benchmark or reference RL, absolute reduced levels cannot be determined.
  However, relative height differences between consecutive points can be computed using the Rise and Fall method.

• The formula used: Rise or Fall = Previous Reading − Next Reading

  • A positive result indicates a rise in level.

  • A negative result indicates a fall in level.

Calculation:

Given:

• 1st Reading = 1.325 m (Back Sight – before instrument shift)

• 2nd Reading = 0.985 m (Fore Sight – same setup)

• 3rd Reading = 2.546 m (Fore Sight – after instrument shift)

Rise/Fall from 1st to 2nd Reading: Rise =1.325 − 0.985 = +0.340m (Rise)

Rise/Fall from 2nd to 3rd Reading: Fall = 0.985 − 2.546 = − 1.561m (Fall)

Net Change from 1st to 3rd Point: + 0.340 − 1.561 = − 1.221m (Fall)

Concept:

True difference is given by the following formula:

TD = (δh_PQ when instrument is at Q + δh_PQ when instrument is at P)/2

where,

TD = True Difference

δh_PQ = Apparent difference in elevation between P and Q

Calculation:

When the instrument is at P, apparent height difference = 2.123 - 1.543 = 0.58

When the instrument is at Q, apparent height difference = 1.750 - 1.121 = 0.629

So,

\(TD = \frac{{0.629 + 0.58}}{2} = 0.6045\)

Now, doing the adjustment,

When the instrument is at Q, staff reading at Q = 1.750

So, Adjusted reading = 1.750 - TD = 1.750 - 0.6045 = 1.1455 = 1.146 m

Explanation:

Hypsometry

Definition: Hypsometry is the method of determining the heights of mountains, hills, or other elevated terrains by observing the temperature at which water boils. This technique is based on the principle that the boiling point of water decreases as altitude increases due to the reduction in atmospheric pressure.

Working Principle:

The principle of hypsometry relies on the relationship between atmospheric pressure and the boiling point of water. As altitude increases, atmospheric pressure decreases, which, in turn, lowers the boiling point of water. By measuring the temperature at which water boils at a particular location and comparing it with the standard boiling point at sea level (100°C), the altitude of the location can be determined. This method is particularly useful in remote or rugged terrains where other methods of levelling might not be feasible.

The mathematical relationship between altitude and atmospheric pressure can be used to calculate the elevation. This relationship is derived from the barometric formula, which considers factors such as the decrease in pressure with height and the temperature of the atmosphere.

Advantages:

• Does not require sophisticated equipment; a thermometer and a standard reference chart are sufficient.
• Useful in remote and inaccessible areas where other levelling methods cannot be employed.
• Relatively simple and quick to perform compared to other levelling techniques.

Disadvantages:

• Less accurate compared to other levelling methods, such as spirit levelling or GPS-based techniques.
• Accuracy is affected by variations in atmospheric conditions, such as temperature and humidity.
• Not suitable for applications requiring high precision.

Applications:

• Determining the height of mountains or elevated terrains in geographical surveys.
• Used in exploratory expeditions and mountaineering to estimate elevations.

Explanation:

1. Reciprocal levelling is a surveying technique used to accurately measure the difference in elevation between two distant points, especially when direct line-of-sight measurements are obstructed or when high precision is needed.

2. This technique involves taking readings at both ends of a line and using the average to eliminate errors caused by earth's curvature and atmospheric refraction.

3. By observing the same points from both directions, the inherent errors (like refraction) are effectively cancelled out. The approach minimizes the impact of errors that might otherwise accumulate over long distances.

Additional InformationLongitudinal Sectioning:

1. Definition: Longitudinal sectioning refers to the vertical cross-section along the length of a structure or terrain.

2. Effect on Earth’s Curvature & Refraction: This method does not directly address the issues of earth's curvature or refraction. It is primarily used to represent a profile along the length, which may involve elevation or slope measurements but does not involve compensating for curvature or refraction.

Profile Levelling:

1. Definition: Profile levelling involves measuring the heights of points along a line, typically following the contour of the ground or a specific path.

2. Effect on Earth’s Curvature & Refraction: While profile levelling is used to measure changes in elevation, it doesn't directly compensate for the earth’s curvature or atmospheric refraction. The measurements are typically taken with a level instrument, but it doesn’t specifically correct for these factors over long distances.

Cross Sectioning:

1. Definition: Cross sectioning involves taking vertical slices or sections across a terrain at specific intervals, usually perpendicular to a central line (e.g., a road or railway line).

2. Effect on Earth’s Curvature & Refraction: Cross sectioning is used to understand the profile of the terrain in relation to a central line but does not address the curvature of the earth or the refraction effect in its standard form. It's a method used to study the shape and gradient of the ground.

Explanation:

Leveling staff:

• It is a self-reading graduated wooden rod having a rectangular cross-section. The lower end of the rod is shod with metal to protect it from wear and usually point of zero measurements from which the graduations are numbered.
• Staff are either solid (having a single piece of 3-meter height)  or folding staff (of 4-meter height into two or three pieces)
• The least count of a leveling staff is 5 mm.
• Leveling used with a leveling instrument to determine the difference in height between points or heights of points above a vertical datum.

Important Points

Explanation:

Two peg test:

(i) This method is either for an optical or digital level or a transit being used as a level. If this error is corrected with transit, it also improves the accuracy of its vertical angle readings.

(ii) It is performed to ensure that line of collimation of the telescope is parallel to the bubble tube axis.

Principle:

(i) The basic principle is that since the error in level readings results from the instrument not sighting exactly horizontally, is thus looking up or down at some angle and that this angle is the same whichever way it is sighting: if you place the instrument exactly midway between two-rod sightings, the vertical error reading on the rod is the same for each, thus the difference in reading between the rods will still give you an accurate elevation difference.

Explanation:

Given

We know

Height of Instrument (HI) = RL + Back sight (BS)

RL at any point = HI - Fore Sight (FS)

HI at P = 100 + 1.655 = 101.655 m

RL of Q = HI @ P - FS = 101.655 - (-1.500) = 103.155 m

HI @ Q = RL @Q + BS @ Q = 103.155 + (- 0.950) = 102.205

RL of R = HI @Q - FS @ Q = 102.205 - 0.750 = 101.455 m

Concept:

The height of the instrument is first established by means of taking sight towards the benchmark of known elevation.

1. Height of instrument = R.L of bench mark + Back sight reading
2. Elevation of station = Height of instrument - Fore sight reading

Calculation:

Given:

R.L of benchmark = 100.0 m, Back sight reading = - 2.105 m (staff is inverted)

Fore sight reading = 1.105

Height of instrument = 100 + (-2.105) = 97.895 m

Elevation of plinth = 97.895 - 1.105 = 96.790 m.

Curvature correction is given by:

C_c = 0.0785 × d²

Where,

d = distance in km = 1 km, C_c = Curvature correction in metres

C_c = -0.0785 × 1² = -0.0785

Noted staff reading = 1.565 m

Correct staff reading = Noted staff reading - C_c

Concept:

From the figure

\(tan\;\theta = Ground\;slope = \frac{{difference\;b/w\;length\;of\;staff\;and\;\left( {HI} \right)}}{{Horizontal\;distance}}\)

\(tan\theta = \frac{1}{{10}} = \frac{{4 - 1.5}}{x}\)

Calculations:

Given,

Height of instrument (HI) = 1.5 m

Length of staff = 4 m

Ground slope (down slope) = 1/10

\(tan\;\theta = \frac{{2.5}}{x} = \frac{1}{{10}}\)

x = 25 m.

Explanation:

A relatively fixed point of known elevation above datum is called a benchmark.

Different types of benchmark are as follows:

A G.T.S. (Great Trigonometrical Survey) benchmark is a permanently fixed reference survey station (or point), having known elevation with respect to a standard datum (mean sea level). These are established all over India by Survey of India department with greater precision.

Permanent benchmark is intended to maintain its elevation without change over a long period of time with reference to an adopted datum, and is located where disturbing influences are believed to be negligible.

A temporary benchmark (TBM) is a fixed point with a known elevation used for level control during construction works and surveys. Nails in road seals, or marks on kerb & channel are commonly used as temporary benchmarks.

Concept:

NOTE:

Reciprocal leveling eliminates the error due to collimation and error due to curvature of Earth completely, but the refraction depends upon the atmosphere which may change every minute.

​Reciprocal Leveling:

• ​This technique of leveling work is used to find the exact height difference or to find the exact RL(Reduce level) of the point by equalizing the distance when there is a large obstruction like a river, ponds, lakes, etc. in direction of the survey.

• It eliminates the following errors:

  i) error in instrument adjustments i.e error due to collimation

  ii) the combined effect of Earth's curvature and the refraction of the atmosphere

  iii) variation in the average refraction.

Concept:

According to H. I method or Collimation method,

H.I = R.L + B.S

R.L = H.I - (B.S/F.S)

Where,

H.I height of instrument, R.L = reduced = level, B.S = Backsight, F.S = foresight

Inverted staff reading

When a point for which R.L is to be determined is at a very high level above the line of sight, for example, the roof of a building, chajja, etc the leveling staff should be inverted such that the bottom of leveling staff should touch a point. It is taken as a negative reading.

Height from the base to bottom of inverted staff is kept = B.S - F.S

As staff is inverted, therefore reading of B.S is taken as negative.

Calculation

Given,

B.S = 1.32 m

RL of station = 115.385 m

F.S = -2.835

H.I = R.L +B.S

H.I = 115.385 + 1.32 = 116.705 m

Now, R.L bottom of the bridge deck,

R.L = H.I – F.S

R.L = 116.705 - (- 2.835) = 119.54 m 

Concepts:

Precise Leveling is used for establishing bench marks with high precision at widely distant points.

• It requires the use of highly modern instruments and greatest care in the field.  
• A high grade level equipped with tilting screw, stadia wires and coincidence level etc. and an invar precision leveling staff are commonly required.
• The parallax should be entirely eliminated by correct focusing.
•  The staff should be exactly vertical.  
•  The bubble should be exactly in the centre of its run at the time of taking readings.
•  Lengths of sights are limiting to about 100 m.
• The back sight and fore sight distances should be exactly equal. Stadia readings may be taken for this purpose.
• To avoid error due to settlement of tripod and staff, the back sights and the following fore sights should be taken in quick successions and the order of taking readings is interchanged at alternate set up i.e. at first setting, the back sight is observed first and then the fore sight while at the 2nd setting, the foresight is taken first and then the back sight and so on.

Rod readings are taken against the two horizontal hairs of the diaphragm. This is done in Tachometry Survey in which horizontal and vertical distances are taken.