Vectors and slope stability

Eric Baer (based on material from Baer and Whittington (2006))
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This homework or in-class activity is designed to teach students with little or no experience with vectors, free-body diagrams, or the like to apply vectors to slope stability problems.

Students first learn the basic properties of vectors, vector addition, resolving forces, etc. They then apply these techniques to establish in a simplified way how geologists can determine if a slope is stable, how much loading a slope can withstand to become unstable, and other principles of slope stability determination.

This activity is used in an introductory geohazards course with no pre-requisites. It can be completed in one to two hours.

Used this activity? Share your experiences and modifications

Learning Goals

At the end of this exercise students should be able to:
  • graphically add vectors
  • resolve vectors into perpendicular components
  • represent forces as vectors
  • determine if a slope is stable or unstable based on the forces acting on it
  • articulate why a steeper slope is less stable than a shallow slope
  • determine, from the mass on a slope and the angle of the slope, how large the downslope force is
  • determine how much weight can be added to a slope before it becomes unstable.

Context for Use

This is used as homework in an introductory geohazards course. I use it after introducing vector notation and using it to help generate a list of factors which impact the stability of a slope. I like it because it allows what is usually a topic that is treated qualitatively (forces in mass movement) to be treated more quantitatively.
It can be done in an evening but often students require some additional assistance from a tutor or someone who has seen vectors before.

Description and Teaching Materials

Vectors and Slope Stability (Microsoft Word 56kB Feb11 06)

This assignment has two parts. The first is a general introduction to vectors, graphical manipulation of vectors and vector addition. The second part of the homework asks students to look at vector diagrams to see if a house is stable on slopes of differing angles. A final question asks students to find the maximum weight for a house on a given slope with known friction.

Teaching Notes and Tips

Students will need protractors, rulers, and perhaps a calculator (if they want to use trigonometry to solve the last question.)
Note that pounds are used as the force units so that students do not need to convert between units of weight and force, as would have to be done if the metric system was used. I found this reduced student errors.


I grade the completed work and place at least one question on a quiz similar to these problems. Another way of assessing is to ask the question why a house on a steep slope is more likely to slide than the same house on a gentle slope.