Unit 6 :- Levelling

Principles of Simple Leveling:

1. Setting Up the Instrument:

   • When a leveling instrument is properly set up, the bubble tube axis and the line of sight are both horizontal, while the vertical axis of the instrument remains vertical.
   • The bubble must be centered and traverse.
   • By sighting a staff placed at a known elevation, the height or elevation of the line of sight can be determined.
   • If the telescope is directed to staffs at unknown points, their readings allow us to calculate the reduced levels of those points.

2. Reduced Level (RL):

   • The reduced level of the line of sight (RL) is calculated as the sum of the instrument’s height (HI) and the staff reading (h1).
   • Reduced level of the point B = RL of line of sight - staff reading (h2).

3. Balancing of Sights:

   • To minimize instrumental errors, the distances from the instrument station to the backsight and foresight points should be approximately equal.
   • Balancing ensures that the effects of errors are mitigated.

Principles of Differential Leveling:

1. Overview:

   • Differential leveling (also known as compound leveling or continuous leveling) is used when points with large elevation differences are far apart.
   • In differential leveling, the instrument is set up at multiple positions, and each setup follows the principles of simple leveling.

2. Change Points (TP):

   • A change point (TP) is a known elevation point where backsight readings are taken.
   • It serves as a reference for calculating the elevation of other points.

3. Backsight (BS) and Foresight (FS):

   • Backsight (BS): The first staff reading taken after setting up the level. It is on a point of known elevation (e.g., a benchmark).
   • Foresight (FS): The staff reading taken on points of unknown elevation.

4. Equidistant Points:

   • For accurate differential leveling, points should be equidistant from the instrument.
   • Errors due to instrumental faults are minimized when the distances are balanced.

In summary, simple leveling establishes horizontal lines, while differential leveling accounts for large elevation differences by using multiple setups and following the principles of simple leveling.

 

Essential instruments used in leveling: the level and the leveling staff.

1. Level (Dumpy Level):

• The dumpy level is a fundamental optical instrument used for both surveying and levelling.
• Components:
  • It consists of a telescopic tube securely held in place by two collars and adjustable screws.
  • The vertical spindle controls the entire instrument.
  • The telescope can be rotated horizontally when positioned on the dumpy level.
  • A bubble tube on top ensures the line of sight remains horizontal.
• Functionality:
  • The dumpy level estimates the relative height of survey locations on the ground.
  • It is used to determine the elevation differences between points.
• Accuracy:
  • The dumpy level is renowned for its high accuracy values, especially in Tacheometric techniques.
  • Accuracy can be as high as 1:4000 for every 100 meters.
• Uses:
  • Crucial in surveying building sites to create level and smooth surfaces.
  • Helps find height differences between two locations.

2. Leveling Staff (Levelling Rod):

• The leveling staff is a graduated wooden or aluminum rod used with a leveling instrument.
• Purpose:
  • Determines the height difference between points or heights of points above a vertical datum.
  • Also known as a stadia rod when used for stadiametric rangefinding.
• Construction and Materials:
  • Leveling rods can be one piece or sectional (shortened for storage or lengthened for use).
  • Aluminum rods telescope inside each other, while wooden rods have sliding connections or hinges.
• Reading a Rod:
  • Graduations can be in imperial or metric units.
  • Metric rods have major numbered graduations in meters and tenths.
  • Imperial graduations include feet, tenths of a foot, and hundredths of a foot.
  • Readings are recorded with millimeter precision.
  • Colors alternate between red and black for each meter of length.  

   

  Definitions of these essential terms related to leveling:

   

• Levelling:

  • Levelling is the process of determining the relative heights or elevations of points or objects on the Earth’s surface.
  • It helps ensure that the ground is level during construction, such as when excavating for laying foundations.

• Datum Surface:

  • The datum surface is a reference plane with respect to which the reduced levels (RL) of other survey points are determined.
  • It can be a real or imaginary location with a nominated elevation of zero.
  • The commonly used datum is mean sea level (MSL).

• Benchmark:

  • A benchmark is a relatively permanent reference point with a known elevation.
  • It serves as a starting point for leveling or as a point for closing checks.
  • Benchmarks can be arbitrary (assumed equal to 100 meters) or permanent (used for significant locations).

• Reduced Level (RL):

  • The reduced level of a point is its height above the datum surface.
  • It is calculated by adding the instrument’s height (HI) to the staff reading (h1).
  • RL of point B = RL of line of sight - staff reading (h2).

• Line of Collimation:

  • The line of collimation is the line connecting the optical center of the telescope to the crosshair.
  • It defines the direction of sight.

• Line of Sight:

  • The line of sight is the path along which the surveyor observes the staff.
  • It determines the elevation of the point being sighted.

• Back Sight (BS):

  • The back sight reading is the first staff reading taken after setting up and leveling the instrument.
  • It is generally taken on a point of known reduced level, such as a benchmark.

• Intermediate Sights:

  • Intermediate sights are readings taken between the back sight and foresight.
  • These points’ RLs are determined using the method mentioned for foresight.

• Foresight (FS):

  • The foresight reading is the last staff reading taken before changing the instrument’s position.
  • It is taken on a point whose RL needs to be determined.
  • Foresight readings are considered negative and are deduced from the height of the instrument to determine the point’s RL.

• Change Point:

  • A change point is a known elevation point where backsight readings are taken.
  • It serves as a reference for calculating the elevation of other points.

   

  Different types of leveling instruments:

• Dumpy Level:

  • The dumpy level is the most commonly used device in leveling.
  • Components:
    • It consists of a telescopic tube securely held in place by two collars and adjustable screws.
    • The vertical spindle controls the entire instrument.
    • The telescope can be rotated horizontally when positioned on the dumpy level.
    • A bubble tube on top ensures the line of sight remains horizontal.
  • Functionality:
    • The dumpy level estimates the relative height of survey locations on the ground.
    • It determines the elevation differences between points.
  • Accuracy:
    • Renowned for its high accuracy values, especially in Tacheometric techniques.
    • Accuracy can be as high as 1:4000 for every 100 meters.
  • Uses:
    • Crucial in surveying building sites to create level and smooth surfaces.
    • Helps find height differences between two locations.

• Tilting Level:

  • The tilting level is another type of leveling instrument.
  • It allows the telescope to be tilted or inclined to different angles.
  • Useful for measuring slopes, gradients, and irregular surfaces.
  • Often employed in construction and engineering projects.

• Automatic Level:

  • The automatic level (also known as an auto level) is a modern instrument.
  • It features a compensator that automatically levels the line of sight.
  • The compensator ensures that the bubble remains centered even if the instrument is slightly out of level.
  • Widely used for precise leveling tasks in construction, land surveying, and roadwork.

   Curvature and Refraction in levelling
  

  1. Curvature:

     • The Earth’s surface is curved, but when we use a leveling instrument, the line of sight provided by the instrument is horizontal, not the actual level line.
     • Due to curvature, points appear lower than they actually are.
     • The error in staff reading due to curvature of the Earth can be calculated as follows:
       • Let (D) be the length of the sight or the distance from the instrument to the staff station in kilometers.
       • The error in staff reading = (0.0785 D^2) meters (where (D) is the distance from the level to the staff in kilometers).
     • The effect of curvature increases the staff reading, so the correction is negative:
       • True staff reading = observed staff reading - (0.0785 D^2).

  2. Refraction:

     • Refraction occurs because rays of light passing through layers of different densities do not remain straight.
     • The ray of light from the staff to the instrument follows a curved path concave towards the Earth.
     • Under normal atmospheric conditions, arc AD may be taken as circular and of radius seven times that of the Earth.
     • Refraction tends to decrease the staff readings.

  3. Combined Effect:

     • Since the effect of curvature is greater than that of refraction, the combined effect is to increase the staff readings.
     • The formula for computing the combined effect of curvature and refraction is:
       • (C + R = 0.021K^2)
       • Where:
         • (C) = correction for curvature
         • (R) = correction for refraction
         • (K) = sighting distance in thousands of feet.
          
       Temporary adjustments of Level
       

       • Leveling Instrument Setup:

         • Before taking any readings, ensure that the leveling instrument (such as a dumpy level or an automatic level) is properly set up.
         • The instrument should be placed on a stable tripod, and the bubble tube should be centered to ensure the line of sight is horizontal.

       • Leveling the Bubble (Bubble Adjustment):

         • The bubble adjustment ensures that the line of sight remains horizontal.
         • Use the leveling screws to center the bubble in the bubble tube.
         • If the bubble is off-center, it indicates that the instrument is not perfectly level. Adjust the screws until the bubble is centered.

       • Line of Collimation Adjustment:

         • The line of collimation is the line connecting the optical center of the telescope to the crosshair.
         • It should be parallel to the horizontal axis of the instrument.
         • Adjust the line of collimation by rotating the telescope until the crosshair aligns with a distant target (e.g., a benchmark).
         • Lock the telescope in this position.

       • Axis Collimation (Horizontal Collimation) Adjustment:

         • The axis collimation ensures that the telescope rotates around a true vertical axis.
         • Aim the telescope at a distant target (e.g., another benchmark) and take a reading (backsight).
         • Rotate the telescope 180 degrees and aim it back at the same target (foresight).
         • If the readings differ, adjust the horizontal axis until the readings match.

       • Crosshair Adjustment:

         • The crosshair (reticle) inside the telescope should be precisely centered.
         • Use the crosshair adjustment screws to align the vertical and horizontal crosshairs.
         • This ensures accurate targeting during readings.
          
       Different types of leveling and their purposes:

       • Simple Leveling:

         • This is the most straightforward operation in leveling. It is used to find the difference in elevation between two points that are both visible from a single position of the level.
         • The primary goal is to determine the height difference between these points.
         • Simple leveling is commonly employed for basic surveying tasks.

       • Differential Leveling (also known as Compound Leveling or Continuous Leveling):

         • Differential leveling comes into play when the points whose elevation needs determination are far apart or when there is a significant difference in elevation.
         • In this method, the instrument is set up at several positions, and at each setup, the principles of simple leveling are applied.
         • It allows accurate measurements over longer distances.

       • Fly Leveling:

         • Fly leveling is a rapid method used for rough leveling.
         • It involves taking readings at various points along a line without setting up the instrument at each point.
         • While it provides quick results, it sacrifices some precision.

       • Reciprocal Leveling:

         • Reciprocal leveling is used when it is impractical to set up the level midway between two points.
         • The difference in elevation between two points is accurately determined by taking two sets of observations.
         • This method ensures accuracy even when the level cannot be positioned exactly midway.

       • Profile Leveling (Longitudinal Leveling or Sectioning):

         • The objective of profile leveling is to determine the elevation of points at known distances apart along a given line.
         • By doing so, an accurate outline of the ground surface (longitudinal profile) can be obtained.
         • It is commonly used for designing roads, railways, and other linear structures.

       • Cross-Sectioning:

         • Cross-sectioning involves leveling to determine the surface undulation or outline of the ground transverse to a given line.
         • Measurements are taken on either side of the line to create a cross-sectional view.
         • Useful for understanding the terrain’s shape and features.

          The two-peg test

         It is a common procedure in surveying and leveling. It involves setting up a level instrument (such as a theodolite or an auto-level) at one peg (benchmark) and then moving it to another peg (usually at a known elevation). Here’s how it works:

       • Initial Setup:

         • Place the level instrument over the first peg (benchmark) and level it using the built-in bubble vials.
         • Take a reading (usually called the “back sight” or “BS”) on a staff rod held at the first peg. This reading gives the elevation of the instrument.

       • Move to the Second Peg:

         • Shift the level instrument to the second peg (the one with a known elevation).
         • Level the instrument again at this new location.

       • Take the Forward Sight (FS):

         • Look through the telescope of the level instrument and take a reading on the staff rod held at the second peg.
         • This reading is called the “forward sight” (FS).

       • Calculations:

         • The difference between the FS and BS readings gives the height difference between the two pegs.
         • If the FS reading is higher than the BS reading, the second peg is higher than the first peg. If it’s lower, the second peg is lower.
         • Add this height difference to the known elevation of the second peg to find the elevation of the first peg.

       The two-peg test is useful for checking the accuracy of the level instrument and ensuring that it is properly calibrated. It’s also used to establish temporary benchmarks during field surveys.