Surveying – Levelling
Sub Engineer Civil Complete Notes + 50 MCQ Test
1. Introduction & Purpose
Primary Purposes
- To determine the elevation of points relative to a reference datum.
- To lay out engineering structures along specified gradients (e.g., roads, pipelines, railways).
- To prepare contour lines and estimate earthwork volumes (cut/fill).
2. Important Terminology
| Term | Definition / Core Concept |
|---|---|
| Datum | An imaginary level surface from which heights/depths are measured (e.g., Mean Sea Level - MSL). |
| Reduced Level (RL) | Vertical elevation of a point above or below the chosen datum surface. |
| Benchmark (BM) | A fixed reference point of known RL used as a starting baseline. |
| Line of Collimation | Line joining the intersection of crosshairs to the optical center of the objective lens and its continuation. |
| Back Sight (BS) | The first staff reading taken after setup on a point of known elevation (BM or CP). |
| Fore Sight (FS) | The last staff reading taken before moving the instrument or finishing the line. |
| Intermediate Sight (IS) | Any staff reading taken between a Back Sight and a Fore Sight. |
| Change Point (CP) | A point where both FS and BS readings are taken to shift instrument stations smoothly. |
| Height of Instrument (HI) | Elevation/RL of the line of sight above the reference datum (HI = RL + BS). |
3. Types of Benchmarks
- GTS Benchmark: Established by Great Trigonometrical Survey of India; highest accuracy, referenced to MSL at Mumbai High.
- Permanent Benchmark: Established by government departments (PWD, Railways) on permanent structures (e.g., bridge piers, post offices).
- Temporary Benchmark: Fixed at the end of a day's work on temporary objects (e.g., tree roots, rock edges) to resume work next day.
- Arbitrary Benchmark: Assumed RL assigned to a local point for small/isolated projects without reference to GTS.
4. Types of Levelling Operations
| Type | Key Feature / Purpose |
|---|---|
| Simple Levelling | Finding elevation difference between two nearby, intervisible points with 1 setup. |
| Differential Levelling | Used when points are far apart, obstacle intervenes, or high elevation difference exists. |
| Fly Levelling | Rapid levelling performed to connect a distant BM to the starting point of a survey (BS & FS only). |
| Check Levelling | Run at the end of a day's work back to the starting benchmark to check accuracy. |
| Profile Levelling | Done along a central line to plot longitudinal profiles (cross-section line alignments). |
| Reciprocal Levelling | Eliminates curvature, refraction, and collimation error across large rivers/valleys without setup in middle. |
5. Instruments & Adjustments
Levelling Instruments
Dumpy Level: Rigid, simple, durable telescope fixed to spindle. Tilting Level: Line of sight tilts relative to vertical axis using micrometer screw. Auto Level: Employs internal compensator (prism system) for automatic leveling.
Levelling Staff
Self-reading or target staff. Smallest division = 0.005 m (5 mm). Minimum reading capability = 5 mm.
Adjustments
- Temporary Adjustments: Done at every setup: (1) Centering (approx), (2) Levelling (using foot screws & bubble tube), (3) Elimination of Parallax (focusing eyepiece and objective).
- Permanent Adjustments: Done when fundamental lines are out of alignment. Tested via Two-Peg Method.
6. Comparison of RL Reduction Methods
| Parameter | Height of Instrument (HI) Method | Rise & Fall Method |
|---|---|---|
| Speed | Faster, saves time (fewer calculations). | Slower, requires consecutive subtractions. |
| Check on IS | No check for intermediate sight calculations. | Full check on IS, BS, and FS! |
| Suitability | Profile levelling with many intermediate sights. | High precision, check levelling, work verification. |
| Arithmetic Check | $\sum BS - \sum FS = \text{Last RL} - \text{First RL}$ | $\sum BS - \sum FS = \sum \text{Rise} - \sum \text{Fall} = \text{Last RL} - \text{First RL}$ |
7. Curvature & Refraction Corrections
Earth Curvature ($C_c$): Makes objects appear lower; correction is ALWAYS subtractive (-).
Atmospheric Refraction ($C_r$): Rays bend downwards; correction is ALWAYS additive (+).
Combined Correction ($C_{comb}$): Net correction is ALWAYS subtractive (-).
(where $D$ is distance in km)
Levelling Formula Master Sheet
Symbols: BS = Back Sight reading, RL = Reduced Level of Benchmark
Unit: Meters (m)
Example: RL = 100.00 m, BS = 1.25 m → HI = 101.25 m
Symbols: Staff Reading = IS or FS
Unit: Meters (m)
Example: HI = 101.25 m, FS = 2.15 m → RL = 99.10 m
Sign Rule: +ve = Rise, -ve = Fall
Unit: Meters (m)
Example: Prev = 1.50 m, Curr = 1.10 m → +0.40 m (Rise)
Usage: Validates internal consistency of reduction work.
Symbols: D = distance in kilometers (km)
Unit: Result in meters (m)
Example: D = 2 km → C = 0.0673 × 4 = 0.269 m (Subtract from Reading)
Symbols: H = height of eye above water level (m), D = distance (km)
Example: H = 4 m → D = 3.85 × 2 = 7.7 km
Symbols: $a_1, a_2$ staff at A; $b_1, b_2$ staff at B from setups 1 & 2
Unit: Meters (m)
Symbols: $\Delta H$ = Height difference, $L$ = Horizontal distance
Example: $\Delta H = 2\text{ m}, L = 100\text{ m} \rightarrow 1\text{ in } 50\text{ or } 2\%$
1. Height of Instrument (HI) Method Problem
Problem: A back sight of 1.455 m is taken on a benchmark of RL 250.000 m. An intermediate sight on point A is 1.205 m and a foresight on change point B is 2.850 m. Calculate RL of point A and point B.
Given:
RL of BM = 250.000 m, BS = 1.455 m
IS on A = 1.205 m, FS on B = 2.850 m
Formulas:
$HI = RL_{BM} + BS$
$RL_A = HI - IS_A$
$RL_B = HI - FS_B$
Calculation:
$HI = 250.000 + 1.455 = 251.455\text{ m}$
$RL_A = 251.455 - 1.205 = 250.250\text{ m}$
$RL_B = 251.455 - 2.850 = 248.605\text{ m}$
Final Answer: RL of A = 250.250 m, RL of B = 248.605 m
2. Reciprocal Levelling True Difference
Problem: Two points A and B are on opposite banks of a river. With level at A, staff readings are: A = 1.150 m, B = 2.550 m. With level at B, staff readings are: A = 0.950 m, B = 2.150 m. Find true level difference between A and B.
Given:
Setup at A: $a_1 = 1.150\text{ m}, b_1 = 2.550\text{ m}$
Setup at B: $a_2 = 0.950\text{ m}, b_2 = 2.150\text{ m}$
Formula:
$H = \frac{(b_1 - a_1) + (b_2 - a_2)}{2}$
Calculation:
$b_1 - a_1 = 2.550 - 1.150 = 1.400\text{ m}$
$b_2 - a_2 = 2.150 - 0.950 = 1.200\text{ m}$
$H = \frac{1.400 + 1.200}{2} = \frac{2.600}{2} = 1.300\text{ m}$
Final Answer: True elevation difference = 1.300 m (Point A is higher than B by 1.300 m).
3. Curvature and Refraction Correction
Problem: Find the true staff reading on a staff held at a distance of 1.5 km when the observed reading is 2.750 m.
Given:
Observed reading = $2.750\text{ m}$, Distance $D = 1.5\text{ km}$
Formula:
$C_{comb} = 0.0673 \cdot D^2\text{ (subtract from observed reading)}$
$\text{True Reading} = \text{Observed Reading} - C_{comb}$
Calculation:
$C_{comb} = 0.0673 \times (1.5)^2 = 0.0673 \times 2.25 = 0.1514\text{ m}$
$\text{True Reading} = 2.750 - 0.1514 = 2.5986\text{ m} \approx 2.599\text{ m}$
Final Answer: Corrected Staff Reading = 2.599 m
MP Sub Engineer Civil - Levelling Test
Test your knowledge with 50 PYQ-style and conceptual questions covering all key levelling concepts.
⏱️ Total Questions: 50
📊 Topics Covered: 17 Standard Modules
🧮 Numerical Questions: 20+
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