Terry E. Tullis

Friction falls towards zero in quartz rock as slip velocity approaches seismic rates

An important unsolved problem in earthquake mechanics is to determine the resistance to slip on faults in the Earths crust during earthquakes. Knowledge of coseismic slip resistance is critical for understanding the magnitude of shear-stress reduction and hence the near-fault acceleration that can occur during earthquakes, which affects the amount of damage that earthquakes are capable of causing. In particular, a long-unresolved problem is the apparently low strength of major faults, which may be caused by low coseismic frictional resistance. The frictional properties of rocks at slip velocities up to 3 mm s-1 and for slip displacements characteristic of large earthquakes have been recently simulated under laboratory conditions. Here we report data on quartz rocks that indicate an extraordinary progressive decrease in frictional resistance with increasing slip velocity above 1 mm s-1. This reduction extrapolates to zero friction at seismic slip rates of ∼1 m s-1, and appears to be due to the formation of a thin layer of silica gel on the fault surface: it may explain the low strength of major faults during earthquakes.

Frictional behavior of large displacement experimental faults

The coefficient of friction and velocity dependence of friction of initially bare surfaces and 1-mm-thick simulated fault gouges ( 400 mm at 25°C and 25 MPa normal stress. Steady state negative friction velocity dependence and a steady state fault zone microstructure are achieved after ∼18 mm displacement, and an approximately constant strength is reached after a few tens of millimeters of sliding on initially bare surfaces. Simulated fault gouges show a large but systematic variation of friction, velocity dependence of friction, dilatancy, and degree of localization with displacement. At short displacement (<10 mm), simulated gouge is strong, velocity strengthening and changes in sliding velocity are accompanied by relatively large changes in dilatancy rate. With continued displacement, simulated gouges become progressively weaker and less velocity strengthening, the velocity dependence of dilatancy rate decreases, and deformation becomes localized into a narrow basal shear which at its most localized is observed to be velocity weakening. With subsequent displacement, the fault restrengthens, returns to velocity strengthening, or to velocity neutral, the velocity dependence of dilatancy rate becomes larger, and deformation becomes distributed. Correlation of friction, velocity dependence of friction and of dilatancy rate, and degree of localization at all displacements in simulated gouge suggest that all quantities are interrelated. The observations do not distinguish the independent variables but suggest that the degree of localization is controlled by the fault strength, not by the friction velocity dependence. The friction velocity dependence and velocity dependence of dilatancy rate can be used as qualitative measures of the degree of localization in simulated gouge, in agreement with previous studies. Theory equating the friction velocity dependence of simulated gouge to the sum of the friction velocity dependence of bare surfaces and the velocity dependence of dilatancy rate of simulated gouge fails to quantitatively account for the experimental observations.

The roles of time and displacement in the evolution effect in rock friction

Room temperature friction experiments on quartzo-feldspathic rocks obey a velocity dependence of strength which consists of two opposite-sensed effects. The second of these effects has a negative velocity dependence and evolves over a characteristic displacement. This evolution effect was originally attributed by Dieterich [1978; 1979] to an underlying time-dependent process but is often described by either of two empirical evolution laws. One depends explicitly on displacement (slip law) and the other retains time dependence (slowness law). The slip law is favored in representing behavior around steady-state as seen in velocity stepping experiments. However, in this study slide-hold-slide tests conducted at different machine stiffnesses show that the evolution effect depends on time, not slip. For the slowness law the coefficient of time-dependent strengthening b is measured directly in slide-hold-slide tests. Existing empirical evolution laws may not be sufficient to describe both near steady-state and non steady-state behavior. Provided a more correct form can be found, time-dependent evolution may improve frictional models of the seismic cycle by reducing the amount of inter-seismic slip.

EUCLIDEAN AND FRACTAL MODELS FOR THE DESCRIPTION OF ROCK SURFACE ROUGHNESS

Accurate description of the topography of rock surfaces is essential because surface roughness affects frictional strength, the flow of fluids in joints and fractures, the seismic behavior of faults, and the formation of gouge and breccia in fault zones. Real rock surfaces can be described using self-similar and self-affine fractal models of surface roughness. If a surface is self-similar, a small portion of the surface, when magnified isotropically, will appear statistically identical to the entire surface. If a surface is self-affine, a magnified portion of the surface will only appear statistically identical to the entire surface if different magnifications are used for the directions parallel and perpendicular to the surface. At least two parameters are required to describe a fractal model; one parameter typically describes how roughness changes with scale, while the other specifies the variance or surface slope at a reference scale. The divider method and the spectral method are in common use to determine the best fit fractal model from surface profile data. Power spectra from self-similar surfaces have slopes of −3 on log-log plots of power spectral density versus spatial frequency, while spectra from self-affine surfaces have slopes other than −3. Power spectra can be interpreted with greater facility if dimensionless amplitude to wavelength ratios are contoured on plots of power spectral density versus frequency. The topography of many natural rock surfaces, including both fractures and faults, is approximately self-similar within the 6.5 order of magnitude wide wavelength band of 10 μm to 40 m. Within smaller wavelength bands, natural rock surfaces may exhibit self-affine behavior.

Constitutive Behavior and Stability of Frictional Sliding of Granite

An understanding of the frictional sliding on faults that can lead to earthquakes requires a knowledge of both constitutive behavior of the sliding surfaces and its mechanical interaction with the loading system. We have determined the constitutive parameters for frictional sliding of initially bare surfaces of Westerly granite, using a recently developed high pressure rotary shear apparatus that allows long distances of sliding and therefore a greater assurance of attaining steady state behavior. From experiments conducted at room temperature and normal stresses of 27–84 MPa several important results have been found. (1) A gouge layer 100 to 200 μm thick was developed from the initially bare rock surfaces after 18 to 70 mm of sliding. (2) The steady state frictional resistance, attained after about 10 mm of sliding, is proportional to the negative of the logarithm of the sliding velocity. (3) Abrup changes in the velocity of sliding result in initial changes in the frictional resistance, which have the same sign as the velocity change, and are followed by a gradual decay to a new steady state value over a characteristic distance of sliding. This velocity weakening behavior is essentially identical with that found by several previous workers on the same material at lower normal stress. (4) Our results are well described by a two state variable constitutive law. The values of the constitutive parameters are quite similar to those found previously at low normal stress, but the characteristic distance is about an order of magnitude smaller than that found at 10 MPa normal stress with thicker layers of coarser gouge. (5) We have approximated our results with a one state variable constitutive law and compared the results with the predictions of existing nonlinear stability analysis; in addition, we have extended the stability analysis to systems possessing two state variables. With such formulations good agreement is found between the experimentally observed and theoretically predicted transitions between stable and unstable sliding. These results allow a better understanding of the instabilities that lead to earthquakes.

Flow laws of polyphase aggregates from end-member flow laws

An incompressible finite element model has been used to study the plane strain deformation of two-phase aggregates deformed by dislocation creep. Input for the model includes the power law flow laws of the two end-member phases and their volume fractions and configuration. The model calculates the overall flow law of the aggregate as well as the stress and strain rate variations within it. The input flow laws were experimentally determined for monomineralic aggregates of clinopyroxene and plagioclase. Results were calculated for a temperature of 1000°C, strain rates from 10−4 to 10−12S−1, and stresses of 1–1000 MPa. For these conditions, the end-member flow laws intersect on a log stress versus log strain rate plot at 10−8S−1. Some runs were made on finite element grids fit to an actual diabase texture (∼64% pyroxene, ∼ 36% plagioclase.) Other runs were made on idealized geometries to test the effects of varying the volume fraction of two phases, shape of inclusions, and relative strengths of inclusion and matrix. Important results include the following: (1) The model results satisfy the requirement that the aggregate strength must lie between the bounds set by the end-member flow laws and those set by assumptions of uniform stress and uniform strain rate. (2) The calculated diabase flow law matches well with that experimentally determined. (3) The aggregate strength within the uniform stress and uniform strain rate bounds is primarily affected by volume fraction, although certain phase geometries can also affect the strength. (4) Although the flow law for an aggregate of power law phases need not be a simple power law, we find it to be a good approximation. We have developed two simple methods of estimating the strength of an aggregate, given the end-member flow law parameters and volume fractions; both give results that agree with the finite element model calculations. (1) One method takes into account the phase geometry and gives a strength for the aggregate at any strain rate. (2) The other method can be used even if the phase geometry is unknown and gives expressions for the aggregate flow law parameters.

The frictional behavior of lizardite and antigorite serpentinites: experiments, constitutive models, and implications for natural faults

Laboratory studies of the frictional behavior of rocks can provide important information about the strength and sliding stability of natural faults. We have conducted friction experiments on antigorite and lizardite serpentinites, rocks common to both continental and oceanic crustal faults. We conducted both velocity-step tests and timed-hold tests on bare surfaces and gouge layers of serpentinite at room temperature. We find that the coefficient of friction of lizardite serpentinite is quite low (0.15–0.35) and could explain the apparent low stresses observed on crustal transform faults, while that of antigorite serpentinite is comparable to other crustal rocks (0.50–0.85). The frictional behavior of both types of serpentinite is well described by a two-mechanism model combining state-variable-dominated behavior at high slip velocities and flow-dominated behavior at low velocities. The two-mechanism model is supported by data from velocity-step tests and timed-hold tests. The low velocity behavior of serpentinite is strongly rate strengthening and should result in stable fault creep on natural faults containing either antigorite or lizardite serpentinite.

Flash heating leads to low frictional strength of crustal rocks at earthquake slip rates.

Extreme temperatures generated over short distances may weaken faults during earthquakes. The sliding resistance of faults during earthquakes is a critical unknown in earthquake physics. The friction coefficient of rocks at slow slip rates in the laboratory ranges from 0.6 to 0.85, consistent with measurements of high stresses in Earth’s crust. Here, we demonstrate that at fast, seismic slip rates, an extraordinary reduction in the friction coefficient of crustal silicate rocks results from intense “flash” heating of microscopic asperity contacts and the resulting degradation of their shear strengths. Values of the friction coefficient due to flash heating could explain the lack of an observed heat flow anomaly along some active faults such as the San Andreas Fault. Nearly pure velocity-weakening friction due to flash heating could explain how earthquake ruptures propagate as self-healing slip pulses.

The frictional behavior of serpentinite: Implications for aseismic creep on shallow crustal faults

Serpentine is common in many active faults and may be responsible for aseismic creep along segments of these faults. To test this, we have conducted a series of velocity stepping experiments to determine the frictional velocity dependence of serpentinite. We slid initially bare, rough surfaces of antigorite serpentinite at room temperature, with velocities from 0.0032 to 10.0 μm/s (1.0×102 to 3.2×105 mm/yr) and normal stresses from 25 to 125 MPa. We find that the velocity dependence of serpentinite undergoes a transition from velocity weakening at fast loading velocities to velocity strengthening at slow velocities and that this change is accompanied by other changes in the constitutive behavior. These results suggest that serpentinite should not be the site of instability initiation during sliding at plate velocities, but may permit propagation of unstable slip initiated elsewhere.

A composite rate‐ and state‐dependent law for rock friction

Existing constitutive laws of rock friction cannot describe both observed strengthening in the absence of slip and frictional behavior around steady-state sliding. Combining existing rate- and state-dependent friction laws, we propose a new friction law, which expresses logarithmically time-dependent healing at sliding velocities smaller than a cut-off velocity V c and approaches the so-called slip law at velocities larger than V c. Numerical simulations show that the new friction law adequately explains experimental results of velocity stepping tests and slide- hold-slide tests, which have widely been used to examine velocity-, time-, and displacement-dependent property of rock friction. Because the new friction law has a simple form and appears appropriate for a wide range of conditions, it is useful for application to numerical modeling of seismic cycles.