Leveling
Differential
Learning Objectives:
- Learn the fundamental concepts of levelling, including benchmarking, line of collimation, and level surface. Grasp the importance of measuring vertical distances accurately in civil engineering projects.
- Gain knowledge about the various instruments used in differential levelling, including the dumpy level, digital level, and automatic level. Learn how to set up and calibrate these instruments.
Levelling is defined as “an art of determining the relative height of different points on, above or below the surface”.
Principle of Levelling:
The principle of levelling is to obtain horizontal line of sight with respect to which vertical distances of the points above or below this line of sight are found.
Objective of levelling:
- To Find the elevation of given point with respect to some assumed reference line called datum.
- To establish point at required elevation respect to datum.
Differential leveling involves measuring the difference in elevation between two points by using a leveling instrument, typically a level and a graduated rod. The process relies on establishing a horizontal line of sight and involves a series of level runs where the instrument is moved along the survey line. The key concepts include the benchmark, which serves as a reference point with a known elevation, and the concept of backsight and foresight readings. Differential leveling is crucial for obtaining accurate elevation data, essential in various civil engineering applications such as topographic mapping, construction layout, and determining the slope of the terrain.
The original uploader was Fantagu at German Wikipedia., CC BY-SA 2.0 DE, via Wikimedia Commons
Theodolite:
This precision surveying tool is employed for measuring horizontal and vertical angles with a high degree of accuracy, aiding engineers in tasks such as boundary surveys, construction layout, and topographic mapping. The theodolite consists of a telescope mounted on a base with graduated circles for azimuth (horizontal angle) and elevation (vertical angle) measurements. It employs a leveling system to ensure the instrument is set horizontally, and its use involves sighting a target through the telescope and recording angular measurements. A theodolite's versatility makes it indispensable in geodetic and construction surveys, providing civil engineers with the means to establish precise angles and positions in various engineering applications.
Fred the Oyster, CC BY-SA 4.0, via Wikimedia Commons
Solved Example: 9035-01
Which of the following is the INCORRECT correction to be applied while determining the difference in elevation between two points, when the observations are from only one point?
A. Axis signal correction
B. Correction for sag
C. Correction for curvature
D. Correction for refraction
Correct Answer: B
Solved Example: 9035-02
Levelling in which levels on each side of the main line at right angles to that line is called?
A. Precise levelling
B. Profile levelling
C. Differential levelling
D. Cross sectioning
Correct Answer: D
Solved Example: 9497-01
When differential leveling is done in order to connect a bench mark to the starting point of the alignment of any road, railway, canal project, it is called:
A. Profile leveling
B. Cross-section leveling
C. Reciprocal leveling
D. Fly leveling
Correct Answer: A
Solved Example: 9497-02
Profile levelling is usually done for determining:
A. Contour of an area
B. Capacity of a reservoir
C. Elevation along straight line
D. Boundary of a property
Correct Answer: C
Solved Example: 9497-03
With the rise of temperature the sensitivity of a bubble tube:
A. Decreases
B. Increases
C. Remains unchanged
D. None of the above
Correct Answer: A
Solved Example: 9497-04
The magnetic bearing of a line is 135° 30'. What is the true bearing if the declination is 5° 15'W?
A. 140° 45'
B. 120° 15'
C. 115° 45'
D. 130° 15'
Correct Answer: D
Solved Example: 9497-05
The theodolite in which the telescope can be revolved through a complete revolution in a vertical plane is called:
A. Titling theodolite
B. Non-transit theodolite
C. Transit theodolite
D. Dumpy level
Correct Answer: C
Solved Example: 9497-06
Two contours of different elevation can unite to form one line only in the case of:
A. Cave
B. Overhanging drift
C. Vertical drift
D. Both (B) and (C)
Correct Answer: C
Solved Example: 9497-07
Which of following is the least count of leveling staff?
A. 0.5 mm
B. 0.15 cm
C. 5 cm
D. 5 mm
Correct Answer: D
Elevations
Elevations are a fundamental concept in the Civil Engineering discipline, encompassing the measurement of vertical distance or height above a reference point, typically the mean sea level.
Engineers use elevations extensively in surveying, design, and construction projects to establish the relative heights of various points on the Earth's surface. Benchmark elevations serve as reference points with known heights, facilitating accurate elevation measurements. Elevation profiles and contour maps are crucial tools in civil engineering, providing a visual representation of the terrain's variation in height. Understanding elevations is essential for grading and drainage design, ensuring proper water flow and structural stability.
Scottthezombie, CC BY-SA 3.0, via Wikimedia Commons
Percent Grades
Learning Objectives:
- Define the concept of "percent grade" in surveying and its significance in road design, construction, and civil engineering.
The grade of a highway is a measure of its incline or slope. The amount of grade indicates how much the highway is inclined from the horizontal. For example, if the section of road is perfectly flat and level, then its grade along that section is zero. However, if the section is very steep, then the grade along the that section will be expressed as a number, usually a percentage, such as 10 percent.
\[\mathrm{Percent\ Grade} = \dfrac{\mathrm{rise}}{\mathrm{run}} \times 100\]This concept of percent grade involves expressing the slope of a surface, typically a road, railway, or landscape, as a percentage based on the vertical rise over a horizontal run. The percent grade is a crucial parameter in civil engineering design and construction, influencing factors such as drainage, accessibility, and safety. Engineers use percent grades to ensure the proper alignment of roads and railways, optimizing transportation infrastructure for efficiency and safety. Understanding percent grades is essential for designing slopes that comply with industry standards and regulations, preventing issues such as erosion and ensuring the stability of structures.
Solved Example: 9036-01
The permissible error (E) for the Precise levelling type with distance (D) in kilometre is given by:
A. $E = \pm 0.025\sqrt{D}$
B. $E = \pm 0.100\sqrt{D}$
C. $E = \pm 0.012\sqrt{D}$
D. $E = \pm 0.006\sqrt{D}$
Correct Answer: D
Solved Example: 9036-02
Keeping the instrument height as 1.5 m, length of staff 4 m, the slope of the ground as 1 in 10, the sight on the down-slope, must be less than________m.
A. 15
B. 20
C. 25
D. 30
Correct Answer: C
Solved Example: 9507-01
If an upgrade of 2% is followed by a downgrade of 2%, and the rate of change of grade is 0.4% per 100 m, the length of the vertical curve will be:
A. 1000 m
B. 600 m
C. 200 m
D. 400 m
Correct Answer: A