Lab 6 - Differential Leveling Assignment (1)

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University of Texas *

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301

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Civil Engineering

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Dec 6, 2023

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CE 301 – Civil Engineering Systems Lab 6 – Differential Leveling Page 1 of 5 Laboratory 6 - Differential Leveling Background Differential leveling is used to find the elevations of given points by taking measurements from a reference value or benchmark. The topography of a land surface must be known for a variety of different projects, such as highway design, stormwater modeling, and building construction. Automatic levels are used to measure the change in elevation between two points. First, a backsight is taken on a point of known elevation, such as a benchmark. This allows us to calculate the elevation of the instrument itself. Next, the telescope is turned to face a point of unknown elevation and a foresight is measured there. The elevation of the new point can be found by subtracting the measured foresight from the elevation of the instrument. The backsight tells us how far above the benchmark our instrument is. The foresight tells us how far below our instrument point A is. Thus: ?? = ? ?𝑀 + ?𝑆 ? ? = ?? − ?𝑆 Where: HI = height of instrument E = elevation BS = backsight FS = foresight Backsight Foresight Automatic Level Level Rod Level Rod Benchmark Point A

CE 301 – Civil Engineering Systems Lab 6 – Differential Leveling Page 2 of 5 Problem Statement In major storms, the runoff of rain that cannot be absorbed by the land can cause flooding, particularly on impermeable surfaces such as roads. The Texas Department of Transportation has hired you to determine whether the majority of water that falls on the plot of land being investigated flows onto San Jacinto or Dean Keeton so they can design a suitable drainage system. You set up a closed circuit of points on the corner of San Jacinto and Dean Keaton. By finding the elevation of each point, you will be able to draw a rough map of the area and estimate the flow of water from the top of the hill onto the two streets. Laboratory Experiment We will use a simple level circuit to establish the elevations of a series of points on the tract of land at the corner of San Jacinto and Dean Keeton. By performing a closed circuit, we can also verify the calibration of our level rods and our ability to use the equipment correctly. Before starting your data collection, calculate the permissible misclosure for this circuit. 𝑃?????????? ?????????? = 0.02√? Where: n = the number of instrument setups When you reach the end of the course, you must compare this value to your observed error. If you are outside of the acceptable range, you must repeat your measurements. Data collection:  Draw a map of the points in relation to each other and the neighboring streets.  Set up the instrument between the benchmark and Point A. Level your instrument using the bulls-eye bubble level.  Place your level rod on the benchmark.  Focus the telescope on the automatic level and read the measurement off the level rod. Record this as your backsight on the benchmark.  Place your level rod on Point A.  Focus the telescope on the automatic level and read the measurement off the level rod. Record this as your foresight on Point A.  Move your automatic level to a spot between Point A and Point B. Take a backsight of A and a foresight of B. Repeat this process at each point.  Close the loop by taking a backsight on Point E and a foresight on the benchmark. This will allow you to calculate an elevation for the benchmark.

CE 301 – Civil Engineering Systems Lab 6 – Differential Leveling Page 3 of 5 Tips for accurate readings:  Setting up the automatic level halfway between points will reduce errors due to the curvature of the earth as discussed in your reading. Pace between the two points you’re measuring to find a midpoint and set your automatic level there.  Your level rod needs to be perfectly vertical to take a correct reading. Sway your level rod back and forth over the point while your teammates are looking through the automatic level. The lowest value seen on the level rod is the correct reading.  Use a small square of wood to provide a firm, even surface to rest the level rod on at each point.  NEVER move your automatic level before you have taken both a backsight and a foresight at a point. Calculations Perform a page check when you finish your measurements to verify your calculations. Page Check: ? ?𝑀 𝐾??𝑤? + ∑ ?𝑆 − ∑ ?𝑆 = ? ?𝑀 𝐹𝑖?𝑎𝑙 Find your loop misclosure by taking the difference between your final, calculated elevation of the benchmark and the initial, known elevation of the benchmark. 𝐿??? ?????????? = ? ?𝑀 𝐹𝑖?𝑎𝑙 − ? ?𝑀 𝐾??𝑤? = 𝛿 A simple adjustment procedure is used to cancel out the error accumulated during data collection. The total loop misclosure, δ , is divided by the number of times the instrument was set up, n. This correction value is applied to each elevation calculated in increasing proportion. Thus: ???????? ????????? ?? ? = ????????? ?? ? − 1 × 𝛿 ? ???????? ????????? ?? ? = ????????? ?? ? − 2 × 𝛿 ? Since the elevation of B was measured relative to the elevation of A, we assume that error has accumulated through two instrument setups. Thus, the elevation of E requires the most adjustment.

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