The Research Experience for Teachers Program /

Activity Title: Landslide Analysis & Mathematical Modeling

Summary:In this lab activity you will be asked to explore a mathematical model to determine debris volume of landslides based upon a photo. You will determine a proportionality constant for a mathematical model through the analysis of debris data from many landslides and a given report of how much volume of debris was removed from a specific I-40 landslide. You will use ImageJ and MS Excel to explore the data to see if you can come up with a mathematical model similar to an actual approach of understanding debris flow of a landslide. Your task is to find an appropriate formula, including an acceptable (based on Excel data analysis) proportionality constant, for the I-40 landslide.

Materials List: Computers, MS Excel Software, ImageJ, access to landslide data (see Associated Zip Files)

Introduction/Motivation: How important would it be to know when a large mound of mud like concrete with trees and rocks is coming your way? Does knowing the area of a landslide help us to also know the volume of the debris? What if you were in charge of cleaning up the slide and your work challenge was to determine how much debris your work crews were going to have to remove from a landslide area? How would predicting the volume help in your decisions?

Pre-Requisite Knowledge:

You should have some basic experience with MS Excel worksheets, and an introduction to ImageJ. Prior to this lesson you should have studied direct and inverse power variations.

Preparation:

  • Obtain the landslide photo image to examine (I-40 Landslide)
  • Research or ask your teacher for a Report that has information about the Volume of Debris removed from the I-40 landslide in North Carolina.
  • Obtain the landslide dataset.

Procedure:

  • Make sure to set your scale on ImageJ before measuring the area of the debris field. Hint: Search for information about the width of interstate highway roads.
  • Open the Landslide Data into Excel (or other spreadsheet program) and analyze the data to see what relationship exists between the volume and area of a debris field.
  • Use known areas and volumes of actual landslides to develop a reasonable constant of proportionality.
  • Use the constant of proportionality and the area of the landslide debris field (from photo) to calculate the debris volume for the I-40 landslide. Compare the calculated volume with the known report of debris volume removed from the slide site (from your research or teacher information).
  • Explain why your mathematical model is reasonable, or not, based on your data analysis.

Lab Activity:

  1. You need to retrieve needed files and data from a file stored on USB Drive or Website(see Associated Zip Files)
  2. You will use Image J to measure the area of the debris in the I-40 landslide photo and use it with the formula V = k A^x to determine the volume of the debris of this particular slide.
  3. You need to manipulate a MS Excel spreadsheet with landslide data to determine the proportionality constant k.
  4. You will use the data columns: length, width, and scarp (length * width * scarp = Volume) to determine volume, then convert area and volume to square kilometers and cubic kilometers to compare with an acceptable value for k = 0.02 where x = 1.4 (if interested in original research, see Associated Zip Files)

Assessment:

Pre-Assessment – Class Discussion:

  • How might we use landslide data to mathematically model how much volume occurs in a landslide debris field given a photograph?
  • What will we need to know to determine volume, starting from a photograph of a landslide area?
  • What will we need to observe in data to predict the type of formula (direct / inverse variation, power models) we will need to model the relationship between Area and Volume in a landslide?

Results/Conclusions

  • Be prepared to present (written/orally) your proportionality constant decision, process, and how you changed your spreadsheet to determine k.