# An Assessment of Hillslope Stability Using the Factor of Safety

#### Summary

Students consider the balance of forces on a hillslope using the Factor of Safety by calculating shear stress and shear strength for an example hillslope and formulating an expression for the factor of safety in an Excel spreadsheet. Students then use this spreadsheet to conduct a sensitivity analysis for the purpose of assessing which variables are most important in determining hillslope stability. A series of short answer questions guide students through this process and a series of reflection questions give students the opportunity to consider assumptions and applicability of the factor of safety to the real world. This is a homework assignment that generally takes 1.5 to 2 hours for students to complete.

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## Learning Goals

• Topical Goals
• Predict hillslope stability using the Factor of Safety (FS)
• Assess which variables involved in calculating FS are mostly likely to change
• Assess the sensitivity of FS to changes in hillslope parameters
• Quantitative Skills Goals
• Formulate the expression for FS in an Excel spreadsheet
• Use Excel to calculate FS within the context of a sensitivity analysis
• Develop a sense of how a change in parameters affects model output

## Context for Use

This activity works well when assigned as a problem set to be completed individually. It can also be incoporated into part of a lab on mass wasting.

The activity is assigned toward the end of a mass wasting unit in an upper-level Earth Surface Processes class. Prior to receiving the assignment students have developed an understanding of hillslope processes and slope stability through lecture, class activities and a hill slope lab. Immediately preceeding the assignment, the concept of mass wasting as a threshold process is introduced. Equations for shear stress and shear strength are also developed for the infinite slope case and the factor of safety is given as a means for assessing the balance between driving and resisting forces.

The activity is followed by a discussion of the reflection piece of the assignment which leads naturally into presentation of the different types of mass wasting events and how they are classified.

## Teaching Notes and Tips

• Present shear stress and shear strength, the concept of mass wasting as a threshold process and the FS equation, as described in the answer key, prior to assigning this activity.
• Emphasize the importance of returning the parameters to their initial values in between each step of the sensitivity analysis.
• Direct students to consider the percent change in FS that results from changing parameters in the sensitivity analysis. This is useful because students sometimes have difficulty comparing the changes that result from altering different variables. But, it can be useful to follow the assignment with a discussion of whether or not percent change in FS is really the most useful means for considering the sensitivity of a hillslope to changes in a parameter. For example, when FS is close to one, even a small percent change can sufficently alter the balance between driving and resisting forces to cause failure.
• Encourage students to collaborate with each other and to discuss their results with classmates.

## Assessment

Grading involves checking for mathematically correct answers and reasonable verbal explanations. In evaluating the reflection questions, I place greater emphasis on demonstration of a reasonable thought process than on arrival at the correct answer.

## References and Resources

Ritter, D.F., Kochel, R.C., and Miller, J.R., 2002, Process Geomorphology (4th ed.): WCB/McGraw-Hill, 560 p.