SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION doi: /nature09348 This section provides supporting information for Reches and Lockner Fault weakening and earthquake instability by powder lubrication. The present topics are (1) experimental set-up; (2) discussion on steady-state friction; and (3) wear calculations. The section includes supplementary figures, labeled by Fig. X_Supp, that are mentioned, but not shown, in the Online Methods section. For sake of clarity, we include here parts of the text already presented in the Online Methods section. EXPERIMENTAL SET-UP Our experimental system was built by Joel Young in the Department of Physics and Astronomy, University of Oklahoma. The system has the essential properties for the study of earthquake weakening: (1) Capability to apply normal stress up to 35 MPa, slip velocity of to 2 m/s, rise-time to full velocity <0.1 s, and unlimited slip distance; (2) Continuous control on slip velocity without the need to periodically reverse the sense of slip 7 ; (3) A ring design of the fault blocks with minor velocity difference (14%) between the outer and inner diameters, eliminating the need for velocity corrections required for solid cylinders 4,5 ; and (4) High frequency, up to 10 khz, continuous monitoring of the laboratory fault behavior, including measurement of normal load, shear load, slip velocity, displacement normal to the fault surface, and sample temperature. Loading system The apparatus frame is 1.8 m tall with two massive decks (Fig. 1_Supp A-C). The decks are connected to each other by four rectangle legs that are internally reinforced. The test cell is placed between the two decks, and it is loaded by the rotary train from below and by normal stress from above (Fig. 1_Supp). The power system includes: (1) A 100 HP three-phase electric motor (Reliance) and controller (Baldor) that provides constant torque of up to 3,000 Nm from 0 RPM to 3300 RPM, and which can accelerate to full speed in 0.1 sec. The motor velocity is monitored and controlled through an 8192 line encoder. (2) The main rotary shaft is powered by the motor with 1:6 velocity reduction sprockets. (3) A 225 kg flywheel that can boost the motor torque. (4) An electromagnetic large clutch (Ogura) that is capable of full engagement in 30 ms. (5) A hydraulic piston system (Enerpac) with axial load up to 9,500 N. (6) Torque monitoring system (Fig. 1_Supp A, B) designed to measure to shear stress in the gouge. Control and monitoring system The control and monitoring system is based on National Instruments components, and it includes a SCXI-1100 with modules 1124 (analog control) 1161 (relay control), 1520 (load cell/strain gage), and 1600 (data acquisition and multiplexer), as well as a USB-6210 (encoder measurements). We use LabView as the control software. Digital sampling rate is up to 10 khz. Load-cells for axial load and torque are made by Honeywell, displacement normal to the fault surface is measured with four eddycurrent sensors made by Lion s Precision (± 1 micron accuracy), temperature measurement is with thermocouples and infrared sensor (Omega), and sample radial velocity is monitored by a Sick-Stegmann encoder. We also monitor the motor velocity and motor torque through channels of the Baldor drive. Samples composition The electron-microprobe (EMP) modal analysis of Sierra White granite is comprised of six main minerals: plagioclase (48%), quartz (38%), alkali-feldspar (5%), ferromagnesian-mica (5%), and muscovite (5%) (Fig. 2_Supp). Mean grain size is about 0.3 mm; mean void space in EMP images is ~4%. Reference to commercial product names should not be construed as an endorsement. Rather, specific components are identified to provide reference for independent determination of machine performance. 1

2 RESEARCH SUPPLEMENTARY INFORMATION E. Figure 1_Supp. The rotary shear apparatus. A. Generalized cross section displaying power train. B. 3D view of the assembled apparatus. C. The apparatus with builder Joel Young. D. Sample blocks assembled in the loading frame. LB-lower block; UB-upper block; SR-sliding ring; TC-thermocouple wires; IR-infra red sensor. E. Sample design shown as vertical cut-through of two cylindrical blocks of solid granite rock. The colors indicate temperature distribution due to frictional heating calculate with finite-element. 2

3 SUPPLEMENTARY INFORMATION RESEARCH Plagioclase 0.5 Biotite Void Space Muscovite Quartz Alkalifeldspar Fig. 2_Supp. Electron-microprobe image of Sierra White granite of present experiments. The electronmicroprobe modal analysis that the rock is comprised of six main minerals: plagioclase (48%), quartz (38%), alkali-feldspar (5%), ferromagnesian-mica (5%), and muscovite (5%). Mean grain size is about 0.3 mm; mean void space in EMP images is ~4%. 3

4 RESEARCH SUPPLEMENTARY INFORMATION STEADY-STATE FRICTION We examined the steady-state friction in 90 experiments in which both velocity and normal stress were maintained constant. The applied velocities range from m/s to 0.97 m/s, and applied normal stress ranges from 0.48 MPa to 7.1 MPa. The slip distance in a single run ranges from 0.1 m to 66 m (Fig. 3_supp). The steady-state friction in these runs is related to the experimentally controlled velocity, V, the normal stress, σ n, and to the spontaneously arising heat, which is a non-trivial function of V, σ n, and friction coefficient. The friction magnitude and its dependence on velocity and heat are discussed in the article. We describe here the evolution of the steady-state friction with respect to slip distance and normal stress. The friction evolution is represented here by the friction change ratio, F r = µ s / µ d, where µ s is the static, initial friction coefficient, and µ d is the dynamic, steady-state friction coefficient. We observed three distinct groups of friction evolution: 1. Runs with large friction drop (F r = 2-3) that evolved during slip distances of 3-10 m (Fig. 4_Supp A); this behavior is observed under slip velocity of a few cm/s (e.g., 4-5 cm/s) and σ n 2.5 MPa. These experiments were run to distances up to 66 m, and their surface temperature increase was on the order of a few degrees. The observed friction reduction is attributed to the development of a weak gouge layer, as discussed in the article. 2. Moderate to negligible friction reduction (F r = ) through slip distances m is observed in experiments for σ n > 2.5 MPa (Fig. 4_Supp B), independent of slip velocity or slip distance in nearly all cases. The higher normal stress leads to faster heating of the experimental fault, and the measured temperature rise (at the thermocouple) was tens of degrees in the low velocity experiments to hundreds of degrees in the high velocity ones. The observed moderate to negligible friction reduction at high speed is attributed to the heat effect that is discussed in detail in the article (also by Sammis et al., 2010, submitted to Pure and Applied Geophysics). 3. Negligible friction reduction or even strengthening (F r = 0.8-1) is observed in experiments of low velocity, V < m/s (Fig. 5). As discussed in the article, slip at low velocity is inefficient in generating a weak gouge layer. Further, time-dependent chemical processes that are very active in the fine-grain gouge powder, may strengthen an existing, weak gouge even during slip (green curve in Fig. 5). The friction evolution presented here and in the article shows that friction magnitude varies with slip velocity, normal stress, frictional heat, and slip history in a complex and interdependent way (e.g., rising/dropping velocity or slide-hold-slide loading). While friction eventually evolves to a steady-state value for a given set of conditions (e.g., Fig. 4_supp), the significance of steady-state friction to fault slip in the field is not clear. Slip velocity along faults is not constant: velocity vanishes when the fault is locked and accelerates and fluctuates intensely during earthquakes (as shown by inversions of strong motion data); even fault creep commonly occurs as transients with accelerating and decelerating phases. Thus, the slip of a fault segment can be approximated by constant velocity only for short periods during which it may develop a quasi steady-state friction. In the present analysis, we presented the quasi steady-state friction during variable velocity experiments (Fig. 1B); this parameter may represent fault behavior better than the true steady-state friction that can be achieved only experimentally. 4

5 SUPPLEMENTARY INFORMATION RESEARCH 100 Distan ce (m ) Slip velocity (m/s) Fig. 3_Supp. Slip distance and slip velocity in 90 experiments. Each point represents an experiment conducted at the indicated constant velocity. 5

6 RESEARCH SUPPLEMENTARY INFORMATION Fig. 4_supp. Examples of friction evolution. Top. Constant velocity at normal stress < 2.4 MPa. Bottom. Examples of both constant and variable velocity at normal stress > 2.4 MPa. 6

7 SUPPLEMENTARY INFORMATION RESEARCH WEAR CALCULATIONS Measuring wear The common methods of wear measurements are by weighing wear products 20, measuring displacement normal to the sliding surfaces 20, 30, 31, or optical techniques. Each method has its limitations: weighing powder is time-consuming and it disrupts the structure of the fault. Following a measurement, it is practically impossible to return to the previous stage. The optical methods are difficult to perform insitu, and require an accurate reference surface. We determine wear by continuously measuring the fault closure/opening with high precision (± 1 µm) sensors. Wear-rate calculations We monitored continuously the change in closure/opening, U, normal to the fault; positive U represents closure. The closure has three contributions: (1) Surface wear, W, indicated by closure (U>0); (2) Thermal expansion (U<0) due to frictional heating; and (3) Compaction or dilation (U<0) of the gouge zone or the granite. We calculate the time-dependent wear-rate as follows. First, the thermal contribution is determined by using the temperature measured with the thermocouple embedded 3 mm from the sliding fault. We monitored the closure due to sample cooling after the sample stops, and used the empirical cooling-closure curve to determine the opening (U<0) during shear. The validity of this procedure was tested by simulating the frictional heat with a specially built ring heater that fits the sliding ring and can heat the sample without fault motion. Example of temperature corrected closure is shown in Fig. 5_Supp. Once the gouge layer is established and its thickness is nearly constant, the excess gouge is ejected from the fault surface, and under this condition, the fault wear is approximately equal to the thermally adjusted closure, W U. Thus, the wear unit is in micron of the thermally corrected closure. Next, we fit a polynomial curve (order of 5-13) to the wear data (Fig. 5_Supp) and take the derivative of this curve with respect to fault slip to obtain the dimensionless wear-rate WR = (dw/dx), where x is fault-parallel slip. There is no universal wear-rate unit, and we use a simple, purely geometric unit, Experimental wear-rate [volume of wear products / area of sliding surfaces] / [slip distance] [thermally corrected closure] / [slip distance]. The wear-rate unit can be dimensionless [m/m], or [10-6 m/m] = [µm/m]; as the later is more suitable for experiments, it is used here. The calculated wear-rates and associated friction in runs # are shown in Fig. 6_Supp. These four tests were run under σ n =3.1 MPa, and their friction variations with temperature are shown in Fig. 3. Increasing velocity steps (up to V=0.16 m/s) were applied in tests and decreasing steps (starting at V=0.15 m/s) were applied in tests Fig. 5_Supp. Wear data (run 670) displaying curves used for wear-rate calculations. 7

8 RESEARCH SUPPLEMENTARY INFORMATION Fig. 6_Supp. The wear-rates and friction in runs # the results of which are also shown in Fig. 3. These four tests were run under σ n =3.1 MPa. Increasing velocity steps (up to V=0.16 m/s) were applied in tests and decreasing steps (starting at V=0.15 m/s) were applied in tests Note the correspondence between variations of friction and wear-rate. 8