1.5 Surveying and Leveling

1.5 Surveying and Leveling

Introduction to Surveying and Leveling

• Surveying is the foundational science and art of determining the relative positions of points on, above, or beneath the Earth's surface

• It is the first and most critical step in any engineering project, from planning and design to construction and monitoring

• This unit covers the core principles of measurement, the essential technique of leveling for establishing elevations, methods for topographic representation, the geometry of horizontal curves for road alignment, and an introduction to modern positioning technologies like GPS and GIS

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1. Fundamentals of Surveying

• Definition: The art and science of making all essential measurements to determine the relative positions of points or physical and cultural details on the Earth's surface and to represent them in a usable form, or to establish the position of points or details

• Primary Objectives:

  • To prepare maps, plans, and charts of the area surveyed

  • To establish boundaries of properties and land parcels

  • To determine areas, volumes, and other related quantities

  • To set out points and lines on the ground for construction

• Principles of Surveying:

  • Working from Whole to Part: Establish a network of control points covering the entire area first (with high precision), then fill in local detail from these controls

  • This localizes errors and prevents their accumulation

  • Location of a Point by Two Independent Measurements: A point can be uniquely located by measuring either two distances, two angles, or one distance and one angle from known reference points

• Classification of Surveying:

  • Based on Purpose:

    • Topographic: Determining natural and man-made features for map making

    • Cadastral: Establishing property boundaries and land parcels

    • Engineering/Construction: Providing data for design and setting out works

    • Hydrographic: Mapping water bodies (seas, rivers, lakes)

  • Based on Instruments Used:

    • Chain/Tape Surveying: Linear measurements only

    • Compass Surveying: Angular measurements with a compass

    • Theodolite Surveying: Precise measurement of horizontal and vertical angles

    • Leveling: Determination of elevations

    • Modern Methods: Total Station, GPS/GNSS, LiDAR

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2. Measurements

2.1 Linear Distance Measurement

• Direct Methods:

  • Chain/Tape Surveying: Uses a 20m or 30m chain, or a steel/invar tape

  • Procedure: Chaining along the line, marking with arrows, booking in the field book

  • Corrections: Must be applied for standard length, temperature, pull (tension), slope, and sag

• Indirect/Optical Methods:

  • Tacheometry: Using a theodolite or total station with a stadia diaphragm to measure distance based on the principle of similar triangles

  • $D = K s + C$

  • Where $K$ is the multiplying constant (usually 100), $s$ is the stadia intercept (staff reading difference), and $C$ is the additive constant

  • Electronic Distance Measurement (EDM): A component of a Total Station that uses infrared, laser, or microwave signals

  • Distance $D$ is calculated from the phase shift or time of flight of the wave

2.2 Vertical Distance Measurement

• Leveling: The primary method for determining the elevation (height above a datum, usually Mean Sea Level) of points

• Differential Leveling: The process of finding the difference in elevation between two points using a leveling instrument and a leveling staff

• Key Terms:

  • Bench Mark (BM): A point of known, permanent elevation

  • Back Sight (BS): The first reading taken on a point of known elevation after setting up the instrument

  • Fore Sight (FS): The last reading taken on a point before moving the instrument

  • Intermediate Sight (IS): Any reading taken between a BS and an FS

  • Height of Instrument (HI): Elevation of the line of sight of the instrument

  • $HI = RL_{BM} + BS$

2.3 Angle and Direction Measurement

• Horizontal Angles:

  • Measured between lines in a horizontal plane

  • Instruments: Compass (magnetic bearing), Theodolite/Total Station (precise measurement)

• Methods of Measurement:

  • Repetition Method: Accumulating the angle by repeated measurements to increase precision

  • Reiteration Method: Measuring all angles around a point to close the horizon (sum should be 360°)

• Vertical Angles:

  • Measured upward or downward from the horizontal plane

  • Zenith Angle: Angle from the vertical upward direction (0° at zenith)

  • Altitude Angle: Angle from the horizontal (0° at horizon, +90° at zenith)

• Bearings and Azimuths:

  • Bearing: The horizontal angle measured clockwise or counterclockwise from a reference meridian (North or South) to a line

  • Expressed as NθE, SθW, etc. (Whole Circle Bearing: 0° to 360° from North)

  • Azimuth: The horizontal angle measured clockwise from a reference direction (usually True North) to the line

  • Ranges from 0° to 360°

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3. Leveling

• Objective: To establish or verify the elevation of points, or to find the difference in height between points

• Types of Levels:

  • Dumpy Level: Robust, widely used in construction

  • Tilting Level: Allows fine tilting of telescope for quick leveling

  • Automatic Level: Uses a self-leveling compensator for faster setup

  • Digital Level: Provides electronic staff reading

• Procedure (Differential Leveling):

  • Set up the level at a location from which both the BM and the new point are visible

  • Take a Back Sight (BS) reading on the staff held on the BM

  • Calculate the Height of Instrument (HI)

  • Take Intermediate Sights (IS) and/or a Fore Sight (FS) on the new point(s)

  • Calculate the Reduced Level (RL) of new points

  • $RL_{new} = HI - Staff\ Reading$

  • When necessary, move the instrument, take a new BS on a Change Point (CP), and repeat

• Booking and Reduction Methods:

  • Height of Collimation (HI) Method: RL = HI - Staff Reading

  • HI is calculated for each setup

  • Rise and Fall Method: The difference between consecutive staff readings is calculated as a "rise" or "fall," which is then applied to the previous RL

• Arithmetic Check: For both methods, the following must hold true

  • $\sum BS - \sum FS = Last\ RL - First\ RL$

• Curvature and Refraction Correction: For long sights (>300m), the combined correction $C_{cr}$ (in meters) is

  • $C_{cr} = 0.0673 D^2$

  • Where $D$ is the sight distance in kilometers

  • This correction is subtracted from the staff reading (or added to the level difference)

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4. Topographic Survey: Principles and Applications

• Objective: To gather data about the natural and man-made features of a terrain and represent them on a topographic map using contour lines

• Contour Line: An imaginary line connecting points of equal elevation above a datum

• Contour Characteristics:

  • Closely spaced contours indicate a steep slope

  • Widely spaced contours indicate a gentle slope

  • Uniformly spaced contours indicate a uniform slope

  • A closed contour with lower values inside indicates a hill

  • A closed contour with higher values inside indicates a depression

• Methods of Contouring:

  • Direct Method: Establishing points on a specific contour line by leveling (e.g., for reservoir boundaries)

  • Accurate but slow

  • Indirect Method: Establishing a grid of spot levels (by leveling or Total Station) and interpolating the contour lines between them

  • This is the most common method

• Applications:

  • Site selection for engineering projects

  • Determining catchment areas and reservoir capacities

  • Earthwork volume calculations (cut and fill)

  • Route planning for roads, canals, and pipelines

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5. Simple Circular Curves

• Purpose: To provide a smooth transition between two intersecting straight alignments (tangents) of a road or railway

• Elements of a Simple Circular Curve:

  • Point of Intersection (PI or I): Point where the two tangents meet

  • Point of Curve (PC or T₁): Point where the curve begins

  • Point of Tangency (PT or T₂): Point where the curve ends

  • Deflection Angle (Δ): The total central angle subtended at the center of the curve by the arc from PC to PT

  • Radius (R): Radius of the circular curve

  • Tangent Length (T): Distance from PI to PC or PT

  • $T = R \tan(\frac{\Delta}{2})$

  • Length of Curve (L): Arc length from PC to PT

  • $L = \frac{\pi R \Delta}{180^\circ}$

  • External Distance (E): Distance from PI to the midpoint of the curve

  • $E = R \left[ \sec(\frac{\Delta}{2}) - 1 \right]$

  • Mid-Ordinate (M): Distance from the midpoint of the long chord to the midpoint of the curve

  • $M = R \left[ 1 - \cos(\frac{\Delta}{2}) \right]$

• Setting Out Methods:

  • Linear Methods (for small curves): Offsets from the long chord or tangents

  • Angular Methods (using Theodolite):

  • Rankine's Method of Tangential Angles (Deflection Angles): Most common

  • The theodolite is set up at PC, and successive points on the curve are located by measuring deflection angles and chord lengths

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6. Principles and Applications of GPS/GIS

6.1 Global Positioning System (GPS) / Global Navigation Satellite System (GNSS)

• Principle: A satellite-based radio-navigation system that provides geospatial positioning anywhere on Earth

• It works on the principle of trilateration

• Components:

  • Space Segment: Constellation of at least 24 satellites orbiting Earth

  • Control Segment: Ground stations that monitor and control the satellites

  • User Segment: GPS receivers used by individuals and industries

• How it Works: The receiver calculates its distance from multiple satellites (using signal travel time) and uses this data to determine its precise 3D location (latitude, longitude, altitude)

• Surveying Applications:

  • Establishing highly accurate control networks

  • Topographic and cadastral surveying

  • Machine guidance and control in construction

  • Deformation monitoring of structures

• Differential GPS (DGPS) & Real-Time Kinematic (RTK): Techniques that use a base station to provide corrections, achieving centimeter-level accuracy

6.2 Geographic Information System (GIS)

• Definition: A computer-based system for capturing, storing, checking, integrating, manipulating, analyzing, and displaying data that is spatially referenced to the Earth

• Key Components:

  • Hardware: Computers, GPS units, scanners

  • Software: ArcGIS, QGIS

  • Data: Spatial Data (where features are) and Attribute Data (what features are)

  • People & Methods

• Principles: GIS links geographic features (points, lines, polygons) on a map with descriptive information in a database

• Applications in Civil Engineering:

  • Urban Planning: Land-use mapping, zoning

  • Transportation: Route planning, traffic management

  • Water Resources: Watershed management, flood modeling

  • Environmental Engineering: Pollution monitoring, site selection

  • Infrastructure Management: Utility mapping (water, sewer, gas lines)

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• Surveying and leveling provide the essential spatial framework for all civil engineering endeavors

• From the basic chain and tape to the sophisticated satellite-based GPS, measurement techniques ensure accuracy from conception to completion

• Understanding contouring and curves enables the modeling and design of the built environment

• GIS empowers engineers to analyze complex spatial relationships, making surveying a dynamic and indispensable field at the intersection of geography, technology, and engineering