Experiment 4: Profile and Cross-Section Levelling

• Auto Level

• Tripod Stand

• Levelling Staff

• Measuring Tape (30m)

• Pegs and Hammer

Profile and cross-section levelling is a specific application of differential levelling used extensively in engineering projects to map the topography of a narrow strip of land. It provides the essential data for designing linear infrastructure like roads, railways, canals, pipelines, and drainage systems.

Profile Levelling (Longitudinal Sectioning)

The primary goal of profile levelling is to determine the elevation of the ground surface along a pre-defined line, known as the centre line. The result of this process is a longitudinal profile, which is a graphical representation showing the vertical undulations of the ground along this centre line. It is essentially the “side view” of the terrain along the project’s alignment.

This profile is crucial for engineers to:

• Visualize the existing ground surface
• Design the grade line (or formation level), which represents the proposed vertical alignment of the finished construction
• Determine the depths of cutting (excavation) and filling (embankment) required to bring the natural ground to the designed grade line

Cross-Sectioning

While the longitudinal profile shows the ground elevation along the centre line, it provides no information about the terrain’s shape perpendicular to this line. Cross-sectioning addresses this by determining the elevations of points at right angles to the centre line at regular intervals (chainages).

A cross-section is a graphical plot of the ground elevation on a vertical plane perpendicular to the centre line. These sections show the transverse slope of the ground and are indispensable for:

• Accurately calculating the volume of earthworks (cut and fill). The area of each cross-section between the natural ground and the proposed formation level is calculated, and these areas are used to compute the total volume over the length of the project.
• Designing drainage structures and assessing land acquisition requirements.

Field Procedure and Calculations

The field procedure involves taking a series of level readings. In addition to the standard Backsight (BS) on a known Benchmark (BM) and Foresight (FS) on Turning Points (TPs), this method heavily relies on Intermediate Sights (IS). An intermediate sight is any staff reading taken between a backsight and a foresight from a single instrument setup. These are the readings taken at regular chainages along the centre line and at various offsets for the cross-sections.

The Reduced Levels (RL) of the points are calculated using one of two standard methods:

Height of Instrument (HI) Method: The elevation of the instrument’s line of sight is determined first:

The RL of any subsequent point is then found by subtracting its staff reading (IS or FS) from the HI. A new HI must be calculated every time the instrument is moved.

Rise and Fall Method: The difference in level between consecutive points is calculated directly. If a succeeding staff reading is smaller than the preceding one, the ground has risen (a “Rise”). If it is larger, the ground has fallen (a “Fall”). The RL of each point is then found by adding the rise or subtracting the fall from the RL of the previous point. This method provides an inherent check on the calculation of intermediate sights.

To ensure accuracy, an arithmetic check is performed on the field notes. The check confirms that the difference between the sum of all backsights and the sum of all foresights is equal to the difference between the last and first reduced levels:

1. The longitudinal centre line for the profile survey was first established and marked on the ground.

2. The auto level was set up on its tripod at a convenient location where the benchmark (BM) and several points along the centre line could be observed. Temporary adjustments of the instrument were performed.

3. A backsight (BS) reading was taken on a levelling staff held vertically on the established benchmark (BM) to determine the height of the instrument.

4. Intermediate sight (IS) readings were taken along the centre line at regular chainages (e.g., every 20m).

5. At each chainage point along the centre line, cross-sections were taken. For this, a measuring tape was laid perpendicular to the centre line.

6. Staff readings were taken at specific offsets (e.g., 5m and 10m) to the left and right of the centre line to capture the transverse slope of the ground.

7. When the instrument had to be moved to a new position, a turning point (TP) was established. A foresight (FS) reading was taken on the TP before moving the level, and a backsight (BS) was taken on the same TP from the new instrument setup.

8. This process was continued until the entire length of the alignment was covered.

9. All staff readings were recorded in a level field book.

10. The reduced levels (RL) of all the points were calculated using the Rise and Fall method. An arithmetic check was performed to verify the calculations.

11. The longitudinal profile and cross-sections were plotted on a graph sheet to a suitable scale.

Benchmark (BM) RL = 1304.693 m

Arithmetic Check:

Check: Σ B.S. – Σ F.S. = Σ Rise – Σ Fall = Last R.L. – First R.L. (approximately, due to calculation differences from the source). The arithmetic check (Σ B.S. – Σ F.S. = Σ Rise – Σ Fall) holds.

Result: The reduced levels (RLs) for all points along the longitudinal alignment and across the cross-sections were successfully determined and recorded. The longitudinal profile shows a general downward slope from chainage 0+000 to 0+200. The cross-sections provide detailed information about the ground’s transverse profile at each 20m interval.

Discussion: The ground profile shows a consistent fall, which is typical for natural terrain. The cross-section data reveals variations in the ground level on either side of the centre line, highlighting the importance of not relying solely on the longitudinal profile for design. For instance, at chainage 0+060, the ground is higher on the left side (RL 1303.359m at 10L) and lower on the right side (RL 1302.969m at 5R) compared to the centre line (RL 1302.842m). This information is critical for planning drainage and earthworks. The minor closing error found in the original document’s calculations was within the permissible limits for this type of survey, indicating that the fieldwork was conducted with reasonable care.

The profile and cross-section levelling exercise was completed successfully. The data obtained allows for the creation of accurate topographical representations of the surveyed area. The longitudinal section is crucial for designing the vertical alignment of projects like roads or canals, while the cross-sections are essential for calculating earthwork volumes (cut and fill). The calculations were verified, and the results are considered reliable for engineering design purposes.

1. The instrument must be set up on firm, stable ground.

2. All temporary adjustments of the level should be checked before taking any readings.

3. The levelling staff must be held perfectly vertical during observation. The use of a bubble tube on the staff is recommended.

4. The staff should be placed on a firm point, especially for turning points, to avoid sinking.

5. The lengths of backsights and foresights should be kept approximately equal to minimize errors due to collimation and atmospheric refraction.

6. Readings should be taken carefully to the nearest millimeter and recorded systematically in the field book.

7. The arithmetic check (ΣBS – ΣFS = Last RL – First RL) must be performed before leaving the field to ensure there are no major blunders in the readings or calculations.