Brian D. Kilgore

Direct observation of frictional contacts: New insights for state-dependent properties

Rocks and many other materials display a rather complicated, but characteristic, dependence of friction on sliding history. These effects are well-described by empirical rate- and state-dependent constitutive formulations which have been utilized for analysis of fault slip and earthquake processes. We present a procedure for direct quantitative microscopic observation of frictional contacts during slip. The observations reveal that frictional state dependence represents an increase of contact area with contact age. Transient changes of sliding resistance correlate with changes in contact area and arise from shifts of contact population age. Displacement-dependent replacement of contact populations is shown to cause the diagnostic evolution of friction over a characteristic sliding distance that occurs whenever slip begins or sliding conditions change.

Imaging surface contacts: power law contact distributions and contact stresses in quartz, calcite, glass and acrylic plastic

A procedure has been developed to obtain microscope images of regions of contact between roughened surfaces of transparent materials, while the surfaces are subjected to static loads or undergoing frictional slip. Static loading experiments with quartz, calcite, soda-lime glass and acrylic plastic at normal stresses to 30 MPa yield power law distributions of contact areas from the smallest contacts that can be resolved (3.5 µm2) up to a limiting size that correlates with the grain size of the abrasive grit used to roughen the surfaces. In each material, increasing normal stress results in a roughly linear increase of the real area of contact. Mechanisms of contact area increase are by growth of existing contacts, coalescence of contacts and appearance of new contacts. Mean contacts stresses are consistent with the indentation strength of each material. Contact size distributions are insensitive to normal stress indicating that the increase of contact area is approximately self-similar. The contact images and contact distributions are modeled using simulations of surfaces with random fractal topographies. The contact process for model fractal surfaces is represented by the simple expedient of removing material at regions where surface irregularities overlap. Synthetic contact images created by this approach reproduce observed characteristics of the contacts and demonstrate that the exponent in the power law distributions depends on the scaling exponent used to generate the surface topography.

Velocity dependent friction of granite over a wide range of conditions

Direct shear sliding experiments on bare ground surfaces of Westerly Granite have been conducted over an exceptionally wide range of sliding rates (10-4 µm/s to 103 µm/s) at unconfined normal stresses (sn) of 5, 15, 30, 70, and 150 MPa. A new sample configuration was developed that permitted measurements at normal stresses of 70 and 150 MPa without immediate sample failure. Measurements of steady-state velocity dependence of friction at velocities between 10-4 and 1 µm/s show similar velocity weakening behavior at all normal stresses, with more negative dependence at lower slip rates. However, at rates above 10 µm/s, velocity weakening is observed only at σn = 30, 70 and 150 MPa, while velocity neutral behavior is observed at σ n = 15 MPa and velocity strengthening is observed at (5, = 5 MPa. The greater velocity weakening observed at velocities below 10-2 µm/s may suggest a transition in competing deformation mechanisms, or the influence of additional mechanisms. The transition to velocity strengthening at high velocity and low normal stress implies that rapid slip on shallow faults could be arrested before resulting in true stick-slip behavior. Stable fault creep and creep events observed at shallow levels on some natural faults may result from this transition in velocity dependence.

Laboratory Observations of Fault Strength in Response to Changes in Normal Stress

Changes in fault normal stress can either inhibit or promote rupture propagation, depending on the fault geometry and on how fault shear strength varies in response to the normal stress change. A better understanding of this dependence will lead to improved earthquake simulation techniques, and ultimately, improved earthquake hazard mitigation efforts. We present the results of new laboratory experiments investigating the effects of step changes in fault normal stress on the fault shear strength during sliding, using bare Westerly granite samples, with roughened sliding surfaces, in a double direct shear apparatus. Previous experimental studies examining the shear strength following a step change in the normal stress produce contradictory results: a set of double direct shear experiments indicates that the shear strength of a fault responds immediately, and then is followed by a prolonged slip-dependent response, while a set of shock loading experiments indicates that there is no immediate component, and the response is purely gradual and slip-dependent. In our new, high-resolution experiments, we observe that the acoustic transmissivity and dilatancy of simulated faults in our tests respond immediately to changes in the normal stress, consistent with the interpretations of previous investigations, and verify an immediate increase in the area of contact between the roughened sliding surfaces as normal stress increases. However, the shear strength of the fault does not immediately increase, indicating that the new area of contact between the rough fault surfaces does not appear preloaded with any shear resistance or strength. Additional slip is required for the fault to achieve a new shear strength appropriate for its new loading conditions, consistent with previous observations made during shock loading.

High‐frequency imaging of elastic contrast and contact area with implications for naturally observed changes in fault properties

During localized slip of a laboratory fault we simultaneously measure the contact area and the dynamic fault normal elastic stiffness. One objective is to determine conditions where stiffness may be used to infer changes in area of contact during sliding on nontransparent fault surfaces. Slip speeds between 0.01 and 10 µm/s and normal stresses between 1 and 2.5 MPa were imposed during velocity step, normal stress step, and slide-hold-slide tests. Stiffness and contact area have a linear interdependence during rate stepping tests and during the hold portion of slide-hold-slide tests. So long as linearity holds, measured fault stiffness can be used on nontransparent materials to infer changes in contact area. However, there are conditions where relations between contact area and stiffness are nonlinear and nonunique. A second objective is to make comparisons between the laboratory- and field-measured changes in fault properties. Time-dependent changes in fault zone normal stiffness made in stress relaxation tests imply postseismic wave speed changes on the order of 0.3% to 0.8% per year in the two or more years following an earthquake; these are smaller than postseismic increases seen within natural damage zones. Based on scaling of the experimental observations, natural postseismic fault normal contraction could be accommodated within a few decimeter wide fault core. Changes in the stiffness of laboratory shear zones exceed 10% per decade and might be detectable in the field postseismically.

A Robust Calibration Technique for Acoustic Emission Systems Based on Momentum Transfer from a Ball Drop

We describe a technique to estimate the seismic moment of acoustic emissions and other extremely small seismic events. Unlike previous calibration tech- niques, it does not require modeling of the wave propagation, sensor response, or signal conditioning. Rather, this technique calibrates the recording system as a whole and uses a ball impact as a reference source or empirical Greens function. To correctly apply this technique, we develop mathematical expressions that link the seismic mo- ment M0 of internal seismic sources (i.e., earthquakes and acoustic emissions) to the impulse, or change in momentum Δp, of externally applied seismic sources (i.e., me- teor impacts or, in this case, ball impact). We find that, at low frequencies, moment and impulse are linked by a constant, which we call the force-moment-rate scale factor C F _ MM0=Δp. This constant is equal to twice the speed of sound in the material from which the seismic sources were generated. Next, we demonstrate the calibration technique on two different experimental rock mechanics facilities. The first example is a saw-cut cylindrical granite sample that is loaded in a triaxial apparatus at 40 MPa confining pressure. The second example is a 2 m long fault cut in a granite sample and deformed in a large biaxial apparatus at lower stress levels. Using the empirical cali- bration technique, we are able to determine absolute source parameters including the seismic moment, corner frequency, stress drop, and radiated energy of these magnitude −2:5 to −7 seismic events.

Slip-pulse rupture behavior on a 2 m granite fault

We describe observations of dynamic rupture events that spontaneously arise on meter-scale laboratory earthquake experiments. While low-frequency slip of the granite sample occurs in a relatively uniform and crack-like manner, instruments capable of detecting high-frequency motions show that some parts of the fault slip abruptly (velocity > 100 mm s−1, acceleration > 20 km s−2) while the majority of the fault slips more slowly. Abruptly slipping regions propagate along the fault at nearly the shear wave speed. We propose that the dramatic reduction in frictional strength implied by this pulse-like rupture behavior has a common mechanism to the weakening reported in high-velocity friction experiments performed on rotary machines. The slip pulses can also be identified as migrating sources of high-frequency seismic waves. As observations from large earthquakes show similar propagating high-frequency sources, the pulses described here may have relevance to the mechanics of larger earthquakes.

Laboratory constraints on models of earthquake recurrence

In this study, rock friction “stick-slip” experiments are used to develop constraints on models of earthquake recurrence. Constant rate loading of bare rock surfaces in high-quality experiments produces stick-slip recurrence that is periodic at least to second order. When the loading rate is varied, recurrence is approximately inversely proportional to loading rate. These laboratory events initiate due to a slip-rate-dependent process that also determines the size of the stress drop and, as a consequence, stress drop varies weakly but systematically with loading rate. This is especially evident in experiments where the loading rate is changed by orders of magnitude, as is thought to be the loading condition of naturally occurring, small repeating earthquakes driven by afterslip, or low-frequency earthquakes loaded by episodic slip. The experimentally observed stress drops are well described by a logarithmic dependence on recurrence interval that can be cast as a nonlinear slip predictable model. The faults rate dependence of strength is the key physical parameter. Additionally, even at constant loading rate the most reproducible laboratory recurrence is not exactly periodic, unlike existing friction recurrence models. We present example laboratory catalogs that document the variance and show that in large catalogs, even at constant loading rate, stress drop and recurrence covary systematically. The origin of this covariance is largely consistent with variability of the dependence of fault strength on slip rate. Laboratory catalogs show aspects of both slip and time predictability, and successive stress drops are strongly correlated indicating a “memory” of prior slip history that extends over at least one recurrence cycle.

Rock friction under variable normal stress

This study is to determine the detailed response of shear strength and other fault properties to changes in normal stress at room temperature using dry initial bare rock surfaces of granite at normal stresses between 5 and 7 MPa. Rapid normal stress changes result in gradual, approximately exponential changes in shear resistance with fault slip. The characteristic length of the exponential change is similar for both increases and decreases in normal stress. In contrast fault normal displacement and the amplitude of small high frequency elastic waves transmitted across the surface follow a two stage response consisting of a large immediate and a smaller gradual response with slip. The characteristic slip distance of the small gradual response is significantly smaller than that of shear resistance. The stability of sliding in response to large step decreases in normal stress is well-predicted using the shear resistance slip length observed in step increases. Analysis of the shear resistance and slip-time histories suggest nearly immediate changes in strength occur in response to rapid changes in normal stress; these are manifest as an immediate change in slip speed. These changes in slip speed can be qualitatively accounted for using a rate-independent strength model. Collectively the observations and model show that acceleration or deceleration in response to normal stress change depends on the size of the change, the frictional characteristics of the fault surface and the elastic properties of the loading system.

Interaction Between Hydraulic Fracture and a Preexisting Fracture under Triaxial Stress Conditions

Enhanced reservoir connectivity generally requires maximizing the intersection between hydraulic fracture (HF) and preexisting underground natural fractures (NF), while having the hydraulic fracture cross the natural fractures (and not arrest). We have studied the interaction between a hydraulic fracture and a polished saw-cut fault. The experiments include a hydraulic fracture initiating from a pressurized axial borehole (using water) that approaches a dry fault that is inclined at an angle θ with respect to the borehole axis. The experiments are conducted on Poly(methyl) Meta Acrylate (PMMA) and Solnhofen limestone, a finely grained (<5 μm grain), low permeability (<10 nD) carbonate. The confining pressure in all experiments is 5 MPa, while the differential stress (1-80 MPa) and approach angle, θ (30, 45, 60, 90°) are experimental variables. During the hydraulic fracture, acoustic emissions (AE), slip velocity, slip magnitude, stress drop and pore pressure are recorded at a 5 MHz sampling rate. A Doppler laser vibrometer measures piston velocity outside the pressure vessel to infer fault slip duration and a strain gauge adjacent to the saw-cut provides a near-field measure of axial stress. For PMMA, the coefficient of friction was 0.30 and sliding was unstable (stick-slip). The approaching HF in PMMA created a tensile fracture detected by AE transducers ~100 μs before the significant stick-slip event (45% stress drop and slip velocity of ~60 mm/s) and was arrested by the fault at all fault orientations and differential stresses, even at 90 fault orientation and 80 MPa differential stress. For Solnhofen limestone, we observed stable sliding at a coefficient of friction of 0.12. In contrast to PMMA, the HF in Solnhofen consistently crossed to the other side of the fault. When the HF crossed the fault, it produced a small stress drop (<10%) and slip velocity of only 0.5 mm/s. Theoretical models by Blanton (1986) and Renshaw and Pollard (1995) predict that HF will be arrested for Solnhofen limestone and cross PMMA 90 fault at 80 MPa differential stress. Although the exact cause for the discrepancy between experiments and the theory is not known, one feature present in the experiments but not considered in the models, is the diffusion of fluid driven by the fault slip. Thus, the formation of a “fluid-filled patch” on the fault surface as it is intersected by the HF may substantially impact the crossing/arrest behavior. The approach angle and differential stress also influence the HF initiation azimuth and breakdown pressure. In most cases, the HF initiation azimuth was normal to the fault strike. These observations suggest that the presence of natural fractures could result in rotation of hydraulic fractures to be more normal to their strike and a subsequent change in the downhole pressure recordings. The latter could be used as a diagnostic tool for predicting this interaction.