All of the ongoing research projects are in one way or the other directed toward gaining a better understanding of earthquake mechanics. Many of these projects are different aspects of laboratory studies of frictional behavior and its causative process.
The following hyperlink list of active research
projects is followed by a more extensive discussion of each one.
Friction at high slip velocity. Most lab experiments have been conducted at slip velocities of 0.1 to 10 microns per second, although we often slide as low as 0.001 microns per second which is approximately the same as the 35 mm/yr average rate of slip on the San Andreas fault. Experiments over this range of slip velocities are relevant to the nucleation phase of the seismic cycle, but tell us little about frictional resistance and processes at velocities at which the dynamic slip during earthquakes occur. Such seismic slip velocities are typically about 1 meter per second, and at this high speed a range of additional processes can occur. Two of these caused by frictional heating are shear melting and the transient increase of pore pressure due to the thermal expansion of the pore fluid. We have been investigating these processes in our laboratory experiments. Having knowledge of these processes and the frictional resistance due to them as a function of slip, slip velocity, permeability, and temperature is important for understanding earthquake dynamics. It seems quite likely that dynamic resistance may be dramatically lower than that at slower slip speeds and if this is the case it has important implications for the expected values of ground accelerations possible during earthquakes and for stress levels in the crust.
During earthquakes we typically expect a combination of high slip velocity, large normal stress, and large displacement. These should lead to substantial frictional heating with typical coefficients of friction of about 0.6, Thus shear melting, leading to formation of pseudotachylites, is expected to be very common, unless the permeability is so low that large transient increases in pore pressure occur, reducing the effective normal stress and thus the shear stress. The extend to which melting on the fault will cause a drop in the shear stress, and how rapidly melting might occur with slip under different conditions is very poorly understood.
Investigation of these effects of frictional heating in the laboratory is not easy, due to the fact that a combination of high normal stress (to keep the rock from fracturing), high slip speed, and large displacement is hard to attain. Our rotary shear apparatus is well suited for such studies because of its ability to combine large slip displacement with high confining pressure. At present our slip speeds are limited to abut 5 mm per second but we have plans to modify the drive system on the apparatus so we can increase this up to 1 m per second.
Although we cannot yet attain seismic slip speeds, we have been doing experiments at slip speed up to 3.2 mm per second, and find some very dramatic and surprising reductions in friction. We have slid to distances of 9 meters and have used normal stresses as high as 112 MPa. We find that the coefficient of friction drops from 0.7 to 0.3 after several hundred mm of slip at normal stress of 28 MPa and down to 0.15 at a normal stress of 112 MPa as is shown in the left figure below.
What is puzzling about all of these results is that the temperature, both the average on the surface and the local "flash temperatures" at asperity contacts, is apparently only 300 to 600 C. Thus, the quartzite samples used should not have been close to their melting temperature, so it is hard to understand why the friction is so low. The most dramatic reduction, that seen at 112 MPa, may be due to some fluxing of melting by fluorine due to the partial breakdown of Teflon in the sliding jacket assembly that keeps the confining gas out of the pore space of the rock. The brown-colored, possibly melted material is shown in the two figures above on the right. (The lower one is a detail of the orange-outlined area in the upper one.) We are currently trying to use graphite instead of teflon to see if we can get a low-friction sliding jacket that will not break down in the presence of considerable frictional heating.
We are in the process of determining the role that fluid chemistry has on the details of the frictional behavior of rock. We are investigating the possibility that we can gain an understanding of the origin of the evolution effect in rate and state friction by changing the fluid chemistry. The question is whether the evolution effect is caused 1) by increases in the real area of contact, or 2) by changes in the quality of the bonding within the existing real contact area, or 3) some combination of 1 and 2. The first explanation initially seems unlikely, since at room temperature plastic flow to increase contact area in silicates is not typically expected. However, the stresses are very high at the small contact areas and so permanent deformation by fracture or dislocation motion may occur, just as it does in weaker metals. The second explanation seem possible, because, although the compressive load that can be born by a contact does not depend on the quality of the bonding, the shear load it can support is strongly affected by the bond quality. Reducing this shear bond strength is how lubricants work.
The fact that the presence of at least traces of water is needed for the evolution effect to be seen, can be interpreted in terms of either explanation 1 or 2 above. In the case of 1, water may either allow easier fracture-aided or dislocation-aided contact area growth, since water enhances both crack propagation and dislocation motion. In the case of 2, water may either act as a contaminant to strong bonding, and its removal might cause evolution to stronger bonds. By varying the chemical environment at the frictional surfaces from that of pure water, it is possible to change the tendency for a solution to adhere to the surfaces and so see if this alters the magnitude of the evolution effect. We are investigating this, in the hopes that altering the chemistry may allow discrimination between explanations 1 and 2; the surface chemistry may not play such an important role in plastic flow.
If changes in contact area are responsible for the evolution effect, as discussed just above, there should be associated changes in the approach of the two surfaces. Thus, if the contact area increases due to brittle or plastic creep under the high normal loads at the contact points, the two surfaces should move closer together. If the change in the real area of contact can be determined from measurement of this approach of the surfaces, this can be used to test if explanation 1 above for the evolution effect works. A way to relate changes in contact area, and hence macroscopic shear resistance, to changes in normal displacement is to calibrate using the changes in normal displacement that occur on changes in applied normal stress. Although the changes in contact area cannot be directly measured this way, it is a fundamental tenet of friction theory that the changes in shear resistance that go with changes in normal stress are due to changes in contact area. Using this line of reasoning, we are measuring the changes in normal displacement that accompany both changes in normal stress and evolution of friction at constant normal stress to see if the area-change explanation matches the prediction.
One of the most interesting results of our experimental work is how the velocity dependence of friction for granite and granite gouge changes with displacement. This is seen in the following figure, which is discussed more fully in our USGS Annual report for Fiscal Year 1999. The lower figure shows that for a 1 mm layer of simulated granite gouge the constitutive parameter a-b changes sign from
positive to negative and back to positive over the first 100 mm of slip. This means that granite gouge starts out velocity strengthening, so sliding would be stable (fault creep), then it become velocity weakening so sliding would be unstable (earthquakes), and then it returns to velocity strengthening. Many repeated experiments show this behavior (Beeler et al., 1996 in Publications). The figure also shows that at long displacements (~1.5 meters) it seems to change sign back to negative, but we need more repeated experiments to confirm this. The figure also shows that initially bare surfaces that generate thin layer of gouge are velocity weakening at all displacements and so earthquakes would always be expected. It is somewhat puzzling that the initial starting configuration for granite affects whether the behavior is stable or unstable, and it may be that after sufficient displacement both initial configurations will converge to the same behavior as the one long displacement experiment on a 1 mm layer of gouge seems to suggest.
The above data on the friction of granite gouge and bares surfaces suggest that the repeated reversals of the sign of the velocity dependence is a characteristic of granular gouge. Some of our unpublished results for the behavior of feldspar gouge shows the surprising result that in some cases this reversal is seen and in others it is not. Preliminary results on quartz gouge suggest that the gouge starts out velocity strengthening, but then switches to velocity weakening and unlike granite gouge remains velocity weakening. Because of the importance of the sign of the velocity dependence for the stability of sliding, it is important to discover if the behavior seen for granite is characteristic of granular materials, or if it is peculiar to granite and/or feldspar. Thus, a series of experiments on quartz gouge are underway to investigate its behavior further.
Another important result of this work is that there is a correlation between the sign of the velocity dependence and whether the deformation is localized or is distributed throughout the gouge. When the velocity dependence is velocity weakening, the deformation is localized, and when it is velocity strengthening, the deformation is broadly distributed. The picture below shows
two samples of feldspar gouge, 1 mm thick, that had an initially vertical band of olivine gouge placed within the feldspar. The amount of shear strain is nearly the same in both samples, but the total displacement is much larger in the lower sample. Most of the localized slip occurred on the boundary-parallel shear near the lower boundary marked with a small "Y." The samples start out with most of the deformation distributed and the frictional response is velocity strengthening, as in the granite gouge data shown in the above diagram. As the sample switches to velocity weakening, the deformation becomes localized.
I have been creating models of Parkfield earthquakes in order to learn whether these models may be helpful in determining what would be expected in terms of premonitory signals prior to earthquakes. The section of the San Andreas fault near the small town of Parkfield California is at the transition between the creeping section of the fault in central California and the presently locked part to the south that last moved in the great 1857 earthquake. Presumably due to the simple loading conditions and the simple straight geometry of the fault in this area, the Parkfield segment has experienced a fairly regular sequence earthquakes in the past 150 years. Thus it has been selected as an area for intensive study and a trial for a scientific earthquake prediction experiment. This fact, and the fact that the Parkfield setting is relatively simple, makes it well suited for making a detailed earthquake model. The model is more likely to be correct with the simple geometry and boundary conditions, and the data gathered from Parkfield can be used to test and improve the model.
In the past, in collaboration with William Stuart of the USGS, I have created a model of the earthquake cycle at Parkfield. I made a 15 minute video of the results of one of these models, and a small cyclic animation of the earthquake model abstracted from this video can be seen by clicking on the following image from the Parkfield model. (Note that the animated file is 600 kb in size, so may take a while to download with a slow modem.)
The model portrayed above has far too few elements and they are too large in size to accurately represent a continuum, since they can fail independently of their neighbors. In addition this model cannot represent microseismicity, foreshocks, or aftershocks in any except the crudest way. In the illustrated model, the smallest "earthquake" that can occur is the motion of a single cell and they are 1 km squares. Thus, both to represent a continuum properly and to allow the model to have a wide range of sizes of earthquakes, as is actually observed at Parkfield, it is necessary to decrease the cell size to something on the order of 1 meter if possible.
The model shown above has about 715 cells. If the 1 km cells that are in the middle of the model were changed to 1 meter cells, there would be about 500 million cells. The computations in such problems typically increase with the square of the number of cells, so if this were the case it would take about 25x1016 times as long to run as the current model, which takes a few hours to run. Thus it is not possible to run such large models with the usual N2 approach. Consequently I have been investigating the use of Fast Multipole methods in which some grouping of cells are used to replace single cells during the computation. More details of this can be found by viewing the PowerPoint slides that I presented at an ACES meeting in Japan, in October, 2000 and those presented at an ACES/GEM workshop in Maui, July 29-August 3, 2001. These slides involve about 1.4 MB and 3.5 MB of data respectively, so if you are using a slow connection to the internet, you may not want to click on the following links to see them. If you wish to see them, click on Japan or Maui to see these two presentations.Fault roughness and Dc
Our earlier measurements of fault roughness have implications for the value of Dc on faults that have not yet been fully explored. In the lab there is a well-defined value for Dc that results from the fact that the laboratory friction surfaces are flat at long wavelengths and rough at smaller wavelengths. The small-wavelength roughness seems to be what controls the value of Dc. The self-similar topography of natural faults, combined with their matedness, as described under our previous work on fault roughness, means that Dc on faults may not be a constant value. It is possible that Dc increases with slip, an idea that is not contained in the present rate and state friction formulation. Whether this is the case or not remains to be investigated, and further analysis of our fault roughness data should help us do this. If the value of Dc cannot be thought of as a constant on natural faults, it might make it easier to understand how it is possible to have such a wide range of sizes of earthquakes.