Introduction to Earth Sciences I
Geophysics Lab # 1
Fragmentation
The process by which naturally occurring Earth materials break into pieces - fragment - is (I claim) a fundamentally non-linear one, perhaps composed of linear individual elements acting together to form a non-linear system.
The physical consequence of this non-linearity is that the detailed physics of how an individual fragment might form does not provide insight that allows us to predict how many fragments will form in a single breaking experiment, or the distribution of their sizes - how many are small, how many are large, how many are in between. That is, the non-linearity of the process leads to an unpredictability in its manifestation. This is much the same system as Per Bak's sand pile in which the detailed examination of any one of the avalanches leads us nowhere in understanding the size or frequency distribution of avalanches.
Despite this we can learn about the fragmentation process and perhaps even the nature of the material being fragmented by studying the behavior of the fragmentation system. That is the purpose of this lab. experiment. You need to do the following:
1. You have several pieces of crockery or some other breakable material. The object is to break them and examine the distribution of sizes of the fragments that result. So first select a large piece (a plate maybe). Put it inside a bag or something that will contain the fragments and drop it from a reasonable height onto hard surface. The inpact puts the object into a critical state.
2. Collect all the pieces, even the smallest, and count the number of pieces.
3. Now the size of the pieces must be determined. There is actually a problem here in defining exactly what we mean by the "size" of a fragment. It would be best to measure their area but that is too hard to do. So you can weigh them with a balance or measure them with calipers. If you measure them with calipers you will need to measure their longest dimension like this:
4. Now , make a table of fragment size and assign a number to each as follows:
Fragment # |
Size (length or weight) |
|---|---|
1 |
16.1 |
2 |
3.4 |
3 |
5.9 |
4 |
2.1 |
| etc. |
5. Re-order the table so that the sizes are in ascending order:
Fragment # |
Size (length or weight) |
1 |
2.1 |
2 |
3.4 |
3 |
5.9 |
4 |
16.1 |
etc. |
6. You will probably see no special ordering in these fragment sizes. The size of the smaller fragments give no real clue to the sizes of the larger fragments. However, if you re-arrange the data again in the following way, and plot them, a relationship may emerge:
Count the number of fragments that exceed a specified size in regular steps. For instance, if you have 20 total fragments ranging in size from 1.1 ounce to 15.5 ounces you can make a new table as follows:
Fragment size |
# fragments exceeding that size |
| 1.0 ounce | 20 (all fragments are bigger than this) |
2.0 |
15 |
3.0 |
12 |
* |
|
* |
|
15.0 |
1 (only one fragment is larger than this) |
7. On the log-log graph paper provided make the horizontal axis the fragment size in regular increments, and the vertical scale the number of fragments that exceed that size. If all goes well the graph will look something like this:
The graph should have a portion that is straight in its central part with droopy tails at both ends.
Question:
What does the existence of the straight portion mean about the relationship between fragment sizes - does it imply some measure of predictability?
Why does the plot have droopy tails?
There are sure to be many fragments much smaller than the size you could pick up and weigh. How could you estimate how many of these very small fragments there are?
8. Repeat 1-7 with a different piece of crockery. You should have a different curve.
Question:
What do the different curves tell you about the fragmentation properties of the two pieces?
Can you estimate the fractal dimansion of the two materials you have broken?
9. If time permits collect up all the pieces of crockery from the first experiment, and re-fragment them by dropping them a second time. Repeat the measuring and graphing exercises 1-7. You now have more smaller pieces because some of the larger pieces got broken in the second drop.
Question:
Do the new fragments fall on a different curve or simple fill in more points at one end of the first? If they form a new curve why do they, if they do not why do they not?
To Topic 1 / To Topic 2 / To Topic 3 / To Topic 4 / To Topic 5