Initial Publication Date: January 11, 2018

# Modeling the Role of Elasticity in Earthquakes

GLENN DOLPHIN (glenn.dolphin@ucalgary.ca) is the Tamaratt Teaching Professor in Geoscience, University of Calgary, Calgary, Alberta.

Understanding what an earthquake is and how one happens is not a straightforward task for novice geoscience learners (Francek, 2013). Understanding the mechanism (elastic rebound) and its unpredictability, in both time and magnitude, can be very challenging. To (safely) afford students an earthquake experience, a model like the earthquake machine (Hubenthal, Braile, & Taber, 2008) can be instructive. This article describes how to build your own earthquake machine and provides ideas for the types of inquiry that you can conduct as you implement such a model in class. A materials list is available in Hubenthal, et al., 2008, and in the online edition of this issue of In the Trenches.

## Making the Earthquake Machine

To assemble an earthquake machine:

• Cut across a ring of large grit belt sandpaper to make one long piece of sandpaper.
• Use duct tape at either end to affix the sandpaper, grit side up, flat on the surface of a desk or lab table. The belt sandpaper can also be affixed to a long, narrow piece of plywood, which allows for manipulation of the slope of the earthquake machine.
• Glue a 4" x 4" piece of sandpaper to one of the sides of a 2" x 4" x 4" wood block.
• Fasten a hook screw into one of the 2" x 4" edges of the block of wood.
• Hook a rubber band to this hook screw (see Figure 1a).
• It is possible to complicate the machine by creating another 2" x 4" x 4" block in the same manner as the first, but with hook screws on opposing 2" x 4" sides of the block. You can place the second block in front of the first (see Figure 1b), attaching the rubber band from the first to the second and then attaching a second rubber band to the other eye screw of the second.

## Using the Earthquake Machine

Place the block sandpaper side down against the belt sandpaper. Work the model by pulling horizontally on the end of the rubber band not attached to the block until the block moves.

In the classroom: It is natural for the students to try to relate the model onto the target concept, i.e., the elastic rebound mechanism of earthquakes. However, without familiarity with the earthquake machine, students will often relate aspects of it incorrectly. (Table 1 lists the strengths and limitations of the model.) For instance, they have a tendency to identify the blocks with continents. This can cause them to make assumptions about what they are doing when they manipulate variables in the model. To mitigate this, it is best to have them become familiar with how it works prior to doing any lab activity. Encourage them to explore the diverse variables present within the model and how each variable affects the behavior of the model. They should try to determine all of the variables, those they can control and those they cannot. Of the ones they can control, they should try to understand how changing a particular variable affects the model's behavior and why. During the time of exploration, they should make sketches of the system and label variables appropriately.

One variable in the model is gravity, which holds the block down onto the sandpaper and affects the amount of friction between the block's sandpaper and the sandpaper below. Gravity cannot be manipulated by the student, but the degree of friction can be by placing an object on the block and altering its weight.

Another variable students may manipulate is the "ease of stretch" of the rubber band, a measure of how much force it takes to deform the band attached to the block. By changing from a thick to thin band, they can increase the ease of stretch. They could also replace the rubber band with a string and see how that affects the behavior of the model.

After students explore with a single block, you could ask them to add a second block. This complicates the system, but better represents where multiple areas of slippage could occur along a single fault and how the motion of one block could be influencedby the motion of another.

Students should then develop a question they can explore that involves manipulating a specific variable. The question should not be a "yes" or "no" question, but involve some description of behavior: "What happens if...?" "What happens if I place more weight on the block?" "How does the speed at which I pull the rubber band affect the movement of the block(s)?" They should then determine a way to to collect data (qualitative or quantitative) related to the manipulated variable, so they can eventually make an evidence-based claim about it, e.g., "The slower I pull on the rubber band, the longer the rubber band stretches before the block begins to move, and the farther the block moves."

Summarize and share all results for the class so students get to see the variation in their inquiries and develop more understanding for the mechanics of the earthquake machine. In general, you will want to draw out the idea of the "stick-slip" behavior of the blocks, the reason for such behavior, and its implications.

(In general, friction causes the blocks to "stick" and allows for the buildup of elastic strain, as the rubber band stretches. The "slip" comes when the force of the pulled rubber band overcomes the force of friction. Here the block lurches forward, releasing energy in terms of heat and sound, and the rubber band returns to a less stretched or even unstretched status.)

To round out this lesson, it would be ideal to incorporate the asperity model (see LaDue and Schwartz in this issue) and the bending rock demonstration (see Hubenthal in this issue). The sandpaper grains on the wood block in contact with the sandpaper grains of the belt sandpaper are the dried pasta asperities, the places where the "stick" happens. The stretching of the rubber band represents the elastic strain occurring in between and among molecules of the rock. There are many, many tiny elastic displacements among the rock molecules. Once the displacements reach a level that the rock can no longer maintain, failure occurs and the rock breaks. The molecules move back (or close to) their pre-deformation configuration, only this time recording motion on either side of the fault. (For more on the earthquake machine, see: http://www.iris.edu/hq/inclass/lesson/developing_arguments_about_earthquake_occurrence).

## References

Francek, M., 2013, Compilation and review of over 500 geoscience misconceptions, International Journal of Science Education, v. 35, no. 1, p. 31-64.

Hubenthal, M., Braile, L., & Taber, J., 2008, Redefining earthquakes and the earthquake machine, The Science Teacher, v. 75, no. 1, p. 32-3.

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