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Keywords:

  • frictional melting;
  • slip weakening;
  • pseudotachylyte

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Details
  5. 3. Results
  6. 4. Discussions
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information

[1] To understand how frictional melting affects fault instability, we performed a series of high-velocity friction experiments on gabbro at slip rates of 0.85–1.49 m s−1, at normal stresses of 1.2–2.4 MPa and with displacements up to 124 m. Experiments have revealed two stages of slip weakening; one following the initial slip and the other immediately after the second peak friction. The first weakening is associated with flash heating, and the second weakening is due to the formation and growth of a molten layer along a simulated fault. The two stages of weakening are separated by a marked strengthening regime in which melt patches grow into a thin, continuous molten layer at the second peak friction. The frictional coefficient decays exponentially from 0.8–1.1 to 0.6 during the second weakening. The host rocks are separated completely by a molten layer during this weakening so that the shear resistance is determined by the gross viscosity and shear strain rate of the molten layer. Melt viscosity increases notably soon after a molten layer forms. However, a fault weakens despite the increase in melt viscosity, and the second weakening is caused by the growth of molten layer resulting in the reduction in shear strain rate of the molten layer. Very thin melt cannot be squeezed out easily from a fault zone so that the rate of melting would be the most critical factor in controlling the slip-weakening distance. Effect of frictional melting on fault motion can be predicted by solving a Stefan problem dealing with moving host rock/molten zone boundaries.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Details
  5. 3. Results
  6. 4. Discussions
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information

[2] Pseudotachylytes have been known for nearly a century, their significance on seismogenic fault motion have been recognized well, and their microstructures and chemistry have been analyzed in detail (Sibson [1975], Allen [1979], Magloughlin and Spray [1992], O'Hara [1992, 2001], and Obata and Karato [1995] among many others). Presence of pseudotachylytes along faults indicates that frictional heating during seismogenic fault motion is large enough to melt rocks, at least in some cases. However, how frictional melting affects the mechanical properties of faults is not understood well even at present. McKenzie and Brune [1972] solved a frictional-heating problem and argued that frictional melting can occur along natural faults. However, simple temperature calculations cannot predict mechanical property of faults during frictional melting. Sibson [1973] performed a simple, but fundamental analysis of frictional heating taking into account of deformation zone and pore pressure build up (thermal pressurization) and discussed why pseudotachylytes along large-scale faults are rare. However, analyses of frictional heating alone cannot predict how frictional melting affects constitutive properties of faults.

[3] On the other hand, Spray [1987, 1988, 1993] pioneered frictional melting experiments on rocks in the late 1980s using a frictional welding machine and reproduced nearly all textural and chemical characteristics of natural pseudotachylytes. Killick [1990] also performed melting experiments on a water-saturated rock using a drilling bit and reproduced pseudotachylytes. However, unfortunately, these workers did not measure mechanical properties of faults during frictional melting. One of us (TS) built a rotary shear high-velocity frictional testing machine in 1990 to study the mechanical properties of faults at high velocities and large displacements, including the effects of frictional melting [Shimamoto and Tsutsumi, 1994]. Shimamoto and Lin [1994] and Lin and Shimamoto [1998] are early efforts using this machine, revealing that frictional melting is nonequilibrium and involves selective melting.

[4] Tsutsumi and Shimamoto [1994, 1996, 1997a, 1997b] report mechanical data and temperature measurements from the first series of high-velocity friction experiments using the above machine. They have shown that frictional melting has effects greater by more than one order of magnitude than any other effects known previously, that the onset of frictional melting imposes marked strengthening of faults, and that steady state friction during frictional melting decreases drastically with increasing slip rate. Goldsby and Tullis [2002] and Di Toro et al. [2004] found dramatic weakening at large displacement and semiseismic slip rates for quartz rocks, possibly due to silica gel formation, using their rotary shear high-pressure apparatus. However, the slip rate was not fast enough to produce frictional melting with their machine.

[5] Tsutsumi and Shimamoto revealed the overall mechanical effects of frictional melting on faults. However, they did not observe deformation textures of melting surfaces closely, so that they could not elucidate the underlying physical processes responsible for the effects of frictional melting. The present work was thus planned to perform detailed textural observations of melting surfaces to identify important physical processes, using the same machine [Hirose et al., 2000; Hirose, 2002; Hirose and Shimamoto, 2003]. We conducted a series of experiments with different total displacements to reveal overall frictional melting processes through textural observations of specimens and then to compare the physical processes with the mechanical behavior. This paper will focus on the effects of frictional melting and will attempt to propose a physical model of frictional melting that enables one to solve thermomechanical processes of frictional melting and to predict the mechanical properties of faults during frictional melting.

2. Experimental Details

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Details
  5. 3. Results
  6. 4. Discussions
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information

2.1. A High-Velocity Frictional Testing Apparatus

[6] All experiments were conducted dry at room temperature using a rotary shear, high-velocity frictional testing apparatus described by Shimamoto and Tsutsumi [1994]. This machine is simple as illustrated in Figure 1. A pair of solid cylindrical or hollow cylindrical specimens with 25 mm in diameter is placed at position 1 in the horizontal loading column, and an axial force up to 10 kN is applied to the specimens with an air pressure-driven actuator (11) in Figure 1a. An unlimited displacement at high velocities is attained by rotating one of the specimens at revolution rates to 1500 rpm with a 7.5 kW motor (2), while the other specimen is kept stationary by using a spline (9). The rotation of the motor is transmitted to the specimen through an electromagnetic clutch (5). Several seconds are needed for the motor to attain a setup speed and the clutch is turned on after the motor speed is reached for a target value. A torque limiter (3) is a safety device to disconnect the motor from the rotary column when the torque exceeds a limit.

image

Figure 1. Schematic sketches showing (a) a rotary shear high-velocity frictional testing machine and (b) a specimen assembly for high-velocity experiments. Points are 1, specimen; 2, motor; 3, torque limiter; 4, torque gauge; 5, electromagnetic clutch; 6, rotary encoder; 7, rotary column; 8, torque-axial force gauge; 9, ball spline; 10, axial force gauge; 11, air actuator; 12, displacement transducer; and 13, water reservoir.

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[7] Axial force, axial shortening of specimens and torque are measured with a force gauge (10), a displacement transducer (12), and torque gauges (4, 8), respectively. All of those data are recorded by an analogue pen recorder and a digital recorder with data sampling rate of 200 kHz. A voltage-controlled voltage source (VCVS)-type noise filter (50 Hz cutoff) is placed on digital recording line to erase high-frequency noises. Only output from torque and axial force gauge (8) is used in this study since the torque gauge (4) measures the torque not only due to the friction along a simulated fault but also due to the friction of ball-bearing supporting axial force (right end of 7 in Figure 1a).

[8] Since the slip rate varies with the radial position of the cylindrical specimens, we have used “equivalent slip velocity”, ve, defined such that τveS gives the rate of total frictional work on a fault with area S, assuming no velocity dependence of the shear stress [Shimamoto and Tsutsumi, 1994]. The ve is given by

  • equation image

where R is the revolution rate of the motor, r1 and r2 are the inner and outer diameters of the hollow cylindrical specimens, respectively. We used hollow cylindrical specimens with outer and inner diameters of 25 and 15 mm, respectively (Figure 1b). The maximum revolution rate of 1500 rpm gives slip rates at outer and inner circumferences of 1.96 and 1.18 m s−1, respectively, and an equivalent slip rate ve of 1.60 m s−1 for the specimens. The equivalent slip rate is referred simply to “slip rate” hereafter.

[9] A big difficulty in high-velocity friction experiments is severe thermal fracturing due to rapid frictional heating which can lower the uniaxial strength of rocks by more than 2 orders of magnitude [Ohtomo and Shimamoto, 1994]. Thermal fracturing is particularly notable for rocks containing quartz that undergoes the α-β transformation at a temperature of 573°C. Even for rocks nearly free from quartz (e.g., gabbro as used in this study), we could apply a normal stress up to about 2.5 MPa above which specimens just fracture. Thus the applied normal stresses in this study is much smaller than that expected for deeper faults, so that we had to increase the total displacements to the order of 100 m to see the entire spectrum of fault behavior during frictional melting. Frictional melting phenomenon is explored in this study in an enlarged view with respect to the displacement than expected for seismogenic fault motion at greater depths under higher normal stresses.

2.2. Samples Used and Experimental Conditions

[10] Experiments were performed on gabbro from India of unknown locality, purchased from a rock dealer. The rock is free from any visible flaws and consists mainly of plagioclase, clinopyroxene, hornblende, biotite, ilmenite and hematite with small amount of orthopyroxene, orthoclase and quartz; see Table 1 for mineralogical composition, determined by point counting under an optical microscope, and for chemical composition of major elements, analyzed by XRF analysis with Rigaku ZSX-101e of Hiroshima University using glass bead specimen. Grains have no crystallographic or shape-preferred orientation and their average size is about 0.51 mm.

Table 1. Major Element Chemistries and Modal Mineralogies of Indian Gabbro Used as Host Rock in the Present Experiments
Protolith ChemistryValue, wt %
SiO252.6
TiO21.0
Al2O313.7
Fe2O313.8
MnO0.2
MgO5.8
CaO10.2
Na2O2.4
K2O0.7
P2O50.1
Total100.5
Protolith MineralogyValue, %
Clinopyroxene37.1
Orthopyroxene2.2
Orthoclase1.7
Plagioclase33.1
Amphibole10.7
Biotite3.9
Quartz1.1
Hematite5.1
Ilmenite4.5
Apatite0.6
Total100.0

[11] For specimen preparation, a hollow cylindrical specimen with outer and inner diameters of 25 and 15 mm, respectively, was drilled from a large block and was cut to about 25 mm in length. Outside surfaces and ends of specimen were then ground with a cylindrical grinder using a 400-grit diamond grinding wheel. Specimen ends were made parallel after being set to the machine by sliding them for about 200 rotations under a normal stress of 0.5 MPa and at a slip rate of 50 mm s−1. Wear materials on the surfaces were splashed away with compressed air. Making specimen ends parallel is critical to avoid distortion of the loading column, to avoid specimen fracturing and to increase the accuracy of torque measurement.

[12] First series of experiments were performed dry at a fixed normal stress of about 1.4 MPa, at a constant slip rate of 0.85 m s−1 and with displacements ranging from 3.1 to 78.6 m (Table 2). Experiments at various displacements are essential to reveal physical processes in the fault zone associated with the mechanical behaviors of simulated faults. Specimens were thin sectioned parallel to the slip direction as closely as possible to observe microstructures under an optical microscope and an analytical scanning electron microscope (SEM) (Figure 1b). Second series of experiments were done at normal stresses of 1.2 to 2.4 MPa and varying the slip rate from 0.85 to 1.49 m s−1 in order to see the effects of normal stress and slip rate (or heat production rate) on the slip-weakening behavior during frictional melting.

Table 2. Summary of All High-Velocity Experiments Reported in This Paper
RunEquivalent Velocity, m/sNormal Stress, MPaTotal Displacement, mPost-First-Peak Displacement, mDisplacement at Second Peak, mPost-Second-Peak Displacment, mdc, mμ at First Peakμ at Second Peakμ at Steady StateThickness of Melt Patches,a mmThickness of Molten Layer,a mm
  • a

    Area-averaged thickness. Thickness directly measured for each patch and took an average shown in parentheses.

HVR0350.851.35.505.45---0.72--1.2 (8.5)-
HVR0340.851.37.237.18---0.83--1.8 (10.3)-
HVR0170.851.47.637.58---0.89--1.6 (7.9)-
HVR0130.851.411.8611.81---0.79--1.8 (7.5)-
HVR0150.851.417.9917.95---0.81--12.7 (19.7)-
HVR0440.851.418.3718.31---0.83--3.8 (8.8)-
HVR0420.851.421.5621.52---0.79--19.8 (20.0)-
HVR0380.851.422.4022.35---0.83--12.6 (16.7)-
HVR0140.851.424.5324.4921.13.4-0.841.07--33 (31)
HVR0160.851.431.3230.7722.29.1-0.851.00--84 (74)
HVR0400.851.438.5838.5325.612.9-0.880.91--104 (81)
HVR0410.851.446.8946.8026.320.6-0.680.88--116 (87)
HVR0430.851.457.7857.7422.535.27.400.870.920.60-108 (82)
HVR0120.851.478.6578.6017.860.89.410.850.990.60-135 (122)
HVR0711.231.3116.60-18.1-4.280.831.090.57--
HVR0781.231.3–2.1121.40-5.0--0.900.830.41–0.45--
HVR0911.071.451.62-24.0-4.690.820.880.54--
HVR0921.491.3–2.469.30-4.8-2.530.930.920.42–0.39--

3. Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Details
  5. 3. Results
  6. 4. Discussions
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information

3.1. High-Velocity Frictional Behaviors of Gabbro

[13] Figure 2 shows a representative mechanical behavior of a simulated fault in gabbro at a slip rate of 0.85 m s−1 and at a normal stress of 1.5 MPa (run HVR012; see Table 2). Two stages of slip weakening are recognized; one after the frictional peak (a to b in Figures 2a and 2b), and the other following the second peak friction (d to e in Figure 2a). The frictional coefficient, μ, at the initial peak friction is around 0.85 at point a (μ at this point ranges 0.68–0.93 for other runs; see Table 2). The initial peak friction is followed by decay in friction in several decimeters to a temporarily steady state near point b. After displacement reaches about 7 m, friction begins to increase toward the second peak friction with μ of 0.99 at point d in Figure 2a (0.84–1.09 for other cases; see Table 2) and the displacement at this peak is 17.8 m (17.8–26.0 m for other cases).

image

Figure 2. (a) A representative mechanical behavior of Indian gabbro at a slip rate of 0.85 m s−1 and a normal stress of 1.5 MPa (run HVR012), shown as a frictional coefficient versus displacement curve, and (b) close-up showing the initial part of curve in Figure 2a. Two stages of slip weakening are recognized (a to b and d to e). Periodic fluctuation on the curves is due to distortion of torque gauge caused by small misalignment of facing specimens. Dashed line in Figure 2a is a least squares fit to the second slip-weakening behavior with equation (2), using Kaleida Graph software. Parameters and standard errors for the parameters are frictional coefficient at the second peak friction μmax = 0.89 ± 0.001, frictional coefficient at steady state friction μss = 0.6 ± 0.0005, and the slip-weakening parameter dc = 9.4 ± 0.08 m.

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[14] Fault surfaces begin to glow bright reddish yellow at around the second peak friction and visible frictional melting begins to occur just after this peak friction is exceeded. Friction decreases gradually toward a residual or steady state friction with μ of about 0.6 (position e in Figure 2a). Melt temperature, measured with K-type thermocouples and a radiation thermometer (see Tsutsumi and Shimamoto [1997b] for the procedures), was about 1140°C at the steady state friction. The electromagnetic clutch was disconnected at a displacement of about 77.5 m, and the specimens slipped about 1.0 m due to the inertia of the rotary column and then immediately got stuck tightly. Shear resistance increased abruptly by a small amount with solidification of melt at the termination of a run (point f).

[15] The mode of strength reduction during the first slip weakening is somewhat variable from run to run. Friction decreases more or less linearly toward temporarily steady state friction in an example in Figure 2b, showing an enlargement of the initial portion of Figure 2a. However, in other cases it decreases nearly exponentially during the first slip weakening. The first slip weakening will be discussed in detail elsewhere.

[16] The second slip weakening is associated with frictional melting and this paper will focus on that. Friction decreases nearly exponentially during the second slip weakening (Figure 2a) and the weakening behavior can be fit well by an empirical equation:

  • equation image

where μmax and μss are frictional coefficients at the second peak friction and residual friction, respectively, d is displacement after the second peak friction (postpeak displacement) and dc is a parameter indicating how rapidly the weakening occurs. Slip-weakening parameter, dc, is defined as the postpeak displacement at which (μ − μss) reduces to exp(−1) ∼ 0.368 of (μmax − μss). The parameter dc for data in Figure 2a is 9.4 ± 0.08 m. We use this parameter instead of slip-weakening distance, Dc, because the displacement at which steady state is attained becomes infinite for an exponential decay of friction. To estimate Dc practically, we define Dc95% as a postpeak displacement at which (μ − μss) reduces to 0.05 of (μmax − μss). Equation (2) yields Dc95% ∼ 3dc (Figure 2a) and this will give a rough idea for the order of Dc. Table 2 gives the parameters dc determined for each run.

[17] The slip-weakening parameter dc has been determined by the same method for other runs performed at normal stresses of 1.2 to 1.5 MPa and at equivalent velocities of 0.85–1.49 m s−1. The results clearly show that dc decreases markedly to the order of 1 m with increasing slip rate or higher heat production rate (Figure 3). The slip-weakening parameter dc is not a fixed parameter, but it varies with slip history and heat production rate.

image

Figure 3. Slip-weakening parameter dc for the second slip weakening plotted against equivalent velocity ve defined by equation (1). A nearly linear relationship, dc = 15.8 (±2.40) [m] − 9.3 (±2.14) [s] ve, holds within the range of ve (correlation coefficient of 0.93). Experiments were done at normal stresses of 1.2 to 1.5 MPa (runs are HVR043, 012, 071, 091, and 092; see Table 2).

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[18] Figure 4 gives shear stress τ plotted against the normal stress σN during the steady state friction (point e in Figure 2a) for three runs with slip rates of 1.23 to 1.49 m s−1. Normal stress was varied during experiments in two of those runs. Shear stress linearly increases with normal stress and τ = 0.15 [MPa] + 0.35 σN holds. The intercept of this relationship is not zero and the frictional coefficient, μ, varies considerable with normal stress. Thus Coulomb's friction law with a constant frictional coefficient does not hold. Our experiments cover from initial rock-on-rock friction to melting stages, but this paper reports experimental data using the term, frictional coefficient, for all cases.

image

Figure 4. A relationship between shear stress τ and normal stress σN on simulated faults in Indian gabbro during the steady state friction after the second slip weakening. A nearly linear relationship, τ = 0.15 (±0.14) [MPa] + 0.35 (±0.08) σN, holds within test conditions (correlation coefficient = 0.91). Byerlee's law, τ = 0.85 σN, is shown as a solid line for comparison.

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3.2. Microtextures of Experimental Fault Zones

[19] Figures 5 and 6 show representative microtextures of simulated fault zones under a polarized microscope and under a SEM, respectively. Prior to the second peak friction, brown colored melt patches (Figures 5a, 5f, and 6a) and broken minerals (Figures 5b and 5g) are present on the fault surface. Note that fault surfaces are not welded prior to this peak friction and are separated after the end of experiments (see white portion in Figure 5a and black portion in Figure 6a between host rocks). Backscattered electron (BSE) image in Figure 6a reveals many fine clasts (or broken fragments) even below 1 μm in size contained in the melt patches. The melt patches are distributed sporadically on the fault plane after the first slip weakening, but their number increases with increasing displacement and develop into a thin, continuous molten layer at least just after the second peak friction is exceeded (Figures 5c, 5h, and 6b). The melt patches and molten layer have turned into quenched glass now, but we will use these terms to highlight their origin.

image

Figure 5. (a)–(e) Photomicrographs of thin sections under plane-polarized light showing typical textures of melting surfaces, and (f)–(j) corresponding sketches displaying molten zones by stippled areas. Figures 5a and 5f are brown colored, biotite melt patches (run HVR013), and Figures 5b and 5g are clasts (or broken fragments) of clinopyroxene (HVR017), both prior to the second peak friction. Figures 5c and 5h show a thin, continuous molten layer just after the second peak friction (HVR014); observe that host rocks are separated completely by the molten layer and that melt is injected into the lower side of the host rock at both ends. Figures 5d and 5i are molten layer close to the steady state friction (HVR043), with rounded and embayed melting surfaces and injection features. Figures 5e and 5j exhibit molten layer at the steady state friction (HVR012), with even more complex melting surfaces. Abbreviations are cpx, clinopyroxene; pl, plagioclase; and bt, biotite.

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image

Figure 6. Backscattered electron (BSE) images showing molten zones along simulated faults in Indian gabbro. (a) A melt patch (fused glass) containing very fine clasts along a vertical fault, prior to the second peak friction (run HVR034, pre-second peak regime); fractures formed and host rocks were separated across the black area after the run. (b) A continuous molten layer with injection veins containing many clasts, just after the second peak friction (HVR014, post-second peak regime). (c) Molten layer containing circular-shaped bubbles and many clasts of plagioclase and clinopyroxene with various sizes, and (d) melt along plagioclase-clinopyroxene grain boundaries about 0.2 mm away from the fault, both during the steady state friction (HVR012, steady state regime). All scale bars are 10 μm. Abbreviations are cpx, clinopyroxene; pl, plagioclase; hmt, hematite; ilm, ilmenite; and bu, bubble.

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[20] The fault surfaces are very straight maintaining the original shape of the ground surface just after a continuous molten layer forms (Figures 5c and 5h). Contrary to the pre-second peak regimes, the host rocks are separated completely by a thin continuous film of molten layer in the post-second peak regime (Figure 5c). The molten layer is colored dark brown and contains vesicles and clasts up to 10 μm in size (Figure 6b) and the amount of clasts increases with increasing displacement (Figures 6b and 6c). Many injection veins, similar to natural pseudotachylytes, begin to form adjacent to the molten layer after the second peak friction (Figure 6b).

[21] The molten layer grows in thickness and melting surfaces become more irregular from the second peak friction toward the steady state friction (Figures 5c to 5e and Figures 5h to 5j; see Hirose and Shimamoto [2003] for the fractal analysis of the melting surfaces). Host rocks are not in solid frictional contact and melting surfaces are rounded in shape (Figures 5d, 5e, 5i, and 5j). Some melt begins to form along grain boundaries away from fault zone (Figure 6d) and the linkage of these melts enhances the breakage of host rocks to increase the amount of clasts in the molten layer toward the steady state. Thus the molten layer contains large and often angular clasts near the steady state friction. The clasts are mainly clinopyroxene and plagioclase, but we could not find biotite and hornblende clasts even under BSE images because those minerals with low melting temperature melted preferentially. Melting of those hydrous minerals must have formed bubbles contained in the molten layer (Figures 5d, 5e, 5i, 5j, and 6c). No clear flow textures such as aligned clasts and no localized shear planes can be found in the molten layer (Figure 6c).

3.3. Chemistry of Melts

[22] Figure 7 and Table 3 show how melt compositions changes with increasing displacement. Major chemical elements were analyzed on carbon-coated, polished thin sections using an EPMA (JEOL 733II) of Hiroshima University with a focused beam of about 1 μm in diameter under accelerating voltage and current typically of 15 kV and 18 nA, respectively. The glassy matrix contains many minute fragments (Figures 6a–6c) and it was difficult to analyze only the glassy portion. Thus we avoided fragments and bubbles as much as possible and took an average of about 8 data points as the representative melt composition at various displacements (Table 3).

image

Figure 7. Changes in compositions of major elements of frictional melt as a function of displacement (see Table 3 for the chemical data). Vertical axes show chemical compositions as normalized by corresponding compositions of the protolith (Table 1). Greater changes in compositions prior to the second peak friction, shown as shaded zones, are caused by preferential melting of minerals with relatively low melting points such as biotite and hornblende.

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Table 3. Melt Composition for 14 Specimens With Different Displacementsa
 BulkRun
035034017013015044042038014016040041043012
  • a

    Chemical analyses were made on glassy matrix with an EPMA and results from about eight measurements were averaged to determine the compositions listed here.

Displacement, m 3.14.77.611.918.018.421.622.424.531.438.747.057.978.6
 
Chemical Composition, wt %
SiO252.656.056.353.054.051.255.752.050.249.351.852.351.552.252.8
Al2O31.01.00.81.00.71.40.81.41.51.71.41.01.51.21.2
Fe2O313.717.117.713.514.412.216.114.112.311.412.312.712.512.713.8
MgO13.810.39.513.011.716.09.814.317.117.514.813.015.713.313.3
MnO0.20.10.20.20.20.20.20.20.20.20.20.20.20.20.2
CaO5.84.24.35.95.66.85.05.76.06.96.66.76.26.45.7
TiO210.29.89.910.210.59.810.710.110.610.810.811.010.010.710.2
Na2O2.42.62.72.22.01.82.42.01.61.51.61.72.02.12.2
K2O0.71.00.80.60.70.80.70.91.01.00.80.80.70.70.9
Total100.4102.1102.299.699.8100.3101.4100.7100.3100.2100.399.5100.399.5100.2
 
Calculated Viscosity
Temperature, °C
100077739884470100016153773092699317196470658459591873
11001958649582453791016851778656123168121152217
12005923025373108321865428193951384765
130021737925361260191071418141723

[23] The ratio of weight percentages of each element between melt (glassy matrix) and host rock is useful to characterize melt composition. Figure 7 displays how the ratio changes with slip for 9 major elements. The range of displacement for the second peak friction is shown as vertical stripe in Figure 7. Chemical composition of melt patches are quite variable with displacement; i.e., Fe2O3, MgO, CaO, MnO, and TiO2 contents increase and SiO2, Al2O3 and Na2O contents decrease toward the second peak friction. Percentage of K2O and TiO2 are higher than those in the host rock, whereas Na2O content is much lower than those in the host rock after the second peak friction.

[24] Chemical analysis thus indicates that the chemical compositions of melts vary considerably early in displacement due to selective melting, but that they tend to become nearly constant toward the steady state friction. Such trend in melt chemistry does seem to be reflected on the melt viscosity, as discussed later.

3.4. Geometry and Viscosity of Melt Patches

[25] The early stages of melting are characterized by the formation of melt patches which begin to form just after the first slip weakening. How melt patches grow to form a continuous molten layer is significant because this process causes a rapid and large increase in friction toward the second peak friction. We have thus measured the number of melt patches per fault length (open circles in Figure 8a), averages of the aspect ratio or the thickness-to-width ratio of melt patches (solid circles in Figure 8a), average thickness and width of melt patches (open and solid squares, respectively, in Figure 8b). We also measured fault area Am in percent occupied by melt patches (solid circles in Figure 8c). The horizontal axes in the Figures 8a–8c denote displacement after the first peak friction (point a in Figure 2), denoted hereafter as “post-first peak displacement”. All measurements were made under an optical microscope using thin sections cut nearly parallel to the slip direction for 8 specimens. Fault area occupied by melt patches, Am, was estimated from the total length of fault surface with melt patches relative to the whole measured length of fault on a thin section, assuming that the fraction of molten surface remain the same in the normal direction of the thin section.

image

Figure 8. Geometrical and viscosity data for melt patches during their growth toward a continuous molten layer, plotted against the displacement after the first peak friction. (a) Density of melt patches in open circles (i.e., number of melt patches per 1 mm fault length), and average aspect ratio of melt patches in solid circles (i.e., an average of the ratio of thickness to width of melt patches). (b) Average thickness and average width of melt patches. (c) Fraction of fault area occupied by melt patches, Am (solid circles), viscosity of melt patches as estimated assuming the coefficient of solid-solid friction is 0.4 (open circles), the same as the friction just after the first slip weakening, and viscosity estimated for melt patches neglecting contribution from solid-solid friction (open diamonds). Right side of each diagram roughly corresponds to the second peak friction.

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[26] Melt patches increase initially in number from about 0.6 mm−1 to 1.5–2.0 mm−1, whereas the geometry of melt patches (i.e., thickness, width and aspect ratio) remains more or less the same (Figure 8a). Friction increases sharply soon after this increase in the number of melt patches. At a post-first peak displacement of around 15 m, the number of melt patches begins to fall, and the average aspect ratio, the average thickness and average width of melt patches increase toward the second peak friction (Figure 8). This no doubt corresponds to the coalescence of melt patches which leads to the formation of a molten layer.

[27] In summary, melt patches of about 7–10 μm in thickness and of about 110–160 μm in width form initially and increase in number (compare Figure 6a). They begin to coalesce when melt patches become dense and grow in width and thickness. Aspect ratio increases sharply soon due to the coalescence of melt patches, after which melt patches begin to grow in thickness and their thickness reaches about 16–20 μm toward the second peak friction. Fault area occupied by melt, Am, increases from about 10% at the onset of melt patches formation to 70–80% close to the second peak friction where a continuous molten layer forms. Continued growth in molten layer leads to the second slip weakening as shown below.

[28] One cannot determine viscosity of melt patches from slip rate in the experiments, measured shear resistance, and geometrical information on melt patches in Figure 8 since frictional coefficient of solid-solid friction cannot be determined independently. However, if one assumes frictional coefficient (about 0.4) just after the first slip weakening (point b in Figure 2) for the solid-solid friction, our mechanical data and geometry of melt patches yield apparent viscosity of melt patches as 5 to 15 Pa s, assuming linear viscous behavior of melt patches (open circles in Figure 8c). On the other hand, the melt patches seems to be thicker than the surface irregularities (Figure 5a) and melt patches may be imposing most shear resistance. Neglecting the contribution from solid-solid friction completely, the same data yield average viscosity of 15 to 45 Pa s for melt patches (open diamonds in Figure 8c). Real viscosity of melt patches should fall in between the two cases. No contribution from solid-solid friction is unlikely particularly when melt patches occupy less that 20% (a few datum points to the left of Figure 8c), so that high viscosity values for the first two results may not be realistic. Thus viscosity of 5 to 20 Pa s would be a reasonable estimate for viscosity of melt patches at least for later stages of melt patch formation. Melt patches contain clasts and bubbles (e.g., Figure 6a), whose effects must be corrected to estimate viscosity of molten portion itself. We could not correct for those effects because clasts and bubbles in melt patches are too small for accurate measurement of their contents.

3.5. Growth of Molten Layer With Slip

[29] To quantify the growth of the molten zone, we have measured an average thickness of molten layer on photomicrographs or on BSE images of thin sections of specimens with different total displacements. Area average was employed to determine the thickness; i.e., the melt thickness was taken as an area of molten layer divided by the length of fault. Average thickness of melt patches was also estimated in a similar manner; i.e., the average thickness is not the real melt thickness at each melt patch, but it is the melt thickness when all melt patches are stretched evenly to cover the entire fault surface. The average melt thickness is less than 2 μm just after melt patches began to form (see Table 2), although melt patches themselves are 5–20 μm in thickness (see section 3.4).

[30] Figure 9a exhibits how thickness of melt patches (open circles) and thickness of molten layer (solid circles) change with displacement. Melt thickness initially increases at an accelerating rate, the rate of thickness increase reaches at a maximum nearly in the midway of the curve, then the rate of thickness increase begins to decline and the melt thickness approaches nearly a constant value of about 120 μm toward the steady state friction. The overall thickness change can be fit well by a well-known logistic curve:

  • equation image

where T is the average melt thickness of molten zone at a displacement δ just after the first weakening, Tss is the final steady state thickness of molten zones, δc is a constant that specifies how rapidly T approaches Tss, and Tss and a determine the initial melt thickness. Note that the initial growth of molten layer becomes nearly an exponential growth because the second term in the denominator is much larger than 1 when displacement δ is small. This exponential growth nearly corresponds to the onset of coalescence of melt patches and their subsequent increase in thickness (compare Figure 8). The solid line in Figure 9a is a least squares fitting curve with Kaleida Graph software, using equation (3) with δc = 3.7 ± 0.5 m, Tss = 118 ± 4 μm, and a = 1846 ± 1861 μm. Standard error for a is very large and this parameter cannot be determined accurately in the present case. The initial thickness is given approximately by Tss/a in equation (3), and the parameter a becomes very large since the initial thickness is very small.

image

Figure 9. An area-averaged thickness of molten layer plotted (a) against displacement immediately after the first slip weakening at which melt patches begin to form and (b) against displacement after the second peak friction (all runs except for the bottom 4 runs in Table 2 are plotted). Figure 9b also exhibits an average shear strain rate (slip rate divided by the average thickness of molten layer) versus post-second peak displacement. To make a comparison with mechanical data easy, frictional coefficient versus displacement curve in Figure 2a is given in Figure 9b without a vertical scale. Solid line in Figure 9a, and dashed and solid lines in Figure 9b are least squares fits to the relevant data with equations (3), (4), and (5), respectively, using Kaleida Graph software. Values of parameters are given in the text.

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[31] Melt patches develop into a continuous molten layer when their average thickness reaches to about 25 μm (change from open to solid circles in Figure 9a). Hence this is the initial thickness of a continuous molten layer. The positions of second peak friction for all runs fall within a vertical stripe in Figure 9a. Fault weakens as the continuous molten layer grows in thickness after the second peak friction, and the thickness change of the molten layer during the second slip weakening can be expressed as

  • equation image

where T is the average thickness of molten zone at a postpeak displacement d, T0 and Tss are the initial and steady state thicknesses of molten zones, respectively, and dcT is a parameter that specifies how rapidly T approaches Tss (see solid diamonds in Figure 9b). The solid line in the Figure 9b is a least squares fitting curve using equation (4) with dcT = 14 ± 5.5 m, Tss = 131 ± 16 μm while T0 is set to be 25 μm. Equation (3) incorporating the entire thickness change give a smaller thickness change parameter δc than dcT. As for the growth of molten layer, equation (4) seems to fit data better than equation (3) (compare solid circles and solid diamonds with fit curves in Figures 9a and 9b). This is not surprising because there is no reason why the initial exponential increase and exponential decline in thickness have the same characteristic distances, δc and dcT (Figure 9a).

[32] Once average melt thickness is measured, average shear strain rate equation image can be estimated from the melt thickness divided by the slip rate (0.85 m s−1) as displayed by open triangles in Figure 9b. The slip rate is high and molten layer is thin so that the average shear strain rate equation image becomes on the order of 104 s−1 (not 10−4 s−1 as in ordinary deformation experiments). The average shear strain rate decreases nearly exponentially with increasing displacement and can be expressed by a similar equation to (2):

  • equation image

where equation image0m is the average initial shear strain rate just after a continuous molten layer form, equation imagessm is the average shear strain rate at the steady state friction, and dcγ specifies how rapidly equation image0m changes to equation imagessm. The solid line in Figure 7b is a least squares fit using equation (5) with dcγ = 7.6 ± 2.4 m and equation imagessm = (0.6 ± 0.26) × 104 s−1. Since the initial thickness of continuous molten layer was taken as 25 μm, the initial average shear strain rate equation image0m becomes 3.4 × 104 s−1, and this value was used in the curve fitting.

[33] Exponential changes in thickness in equation (4) and in the shear strain rate in equation (5) are similar in form to the exponential decay in friction in equation (2) with the same order of distance (compare dc = 9.4 m). This similarity will be used to estimate slip-weakening distance for natural pseudotachylyte-bearing faults in a separate paper.

3.6. Melt Viscosity During the Growth of Molten Layer

[34] Shear strain rate and melt viscosity should primarily control the shear resistance of a fault after host rocks are separated by a molten layer during the second slip weakening. An apparent viscosity of molten layer at the end of each run was determined by dividing the measured shear stress by the shear strain rate shown in Figure 9b, assuming that the molten layer behaved as a Newtonian fluid. Apparent viscosity (open circles in Figure 10a) notably increases first from about 45 Pa s to slightly over 100 Pa s, decreases by a small amount after the second peak friction and finally increases slightly with increasing displacement toward the steady state friction.

image

Figure 10. (a) Apparent maximum viscosity (open circles) of molten layer, maximum viscosity corrected for bubbles (open squares), and maximum melt viscosity corrected for clasts and bubbles (solid diamonds) plotted against the post-second peak displacement. (b) Comparison of maximum (solid diamonds) and minimum (open diamonds) melt viscosities, both corrected for clasts and bubbles. An area-averaged thickness is used to estimate shear strain rate to estimate the maximum melt viscosity; that is, the whole molten zone is included in determining the thickness of molten layer. Whereas melt thickness across two lines connecting roughness peaks on both host rock/molten layer interfaces is used to estimate the minimum viscosities. The latter gives a thinner molten layer, a greater shear strain rate, and a lower viscosity than the former. For reference, mechanical data in Figure 2a are shown without vertical scale.

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[35] The molten layer contains clasts and bubbles and the apparent viscosity has to be corrected for them to determine the viscosity of melt itself. Figure 11 gives proportion of clasts and bubbles within the molten layer as estimated by measuring the total area occupied by clasts and bubbles on microphotographs and BSE images. Amount of bubbles (solid circles) first increases abruptly and then decreases slowly, whereas the amount of clasts (open diamonds) continues to increase with increasing post-second peak displacement.

image

Figure 11. Proportions of clasts (or broken fragments) and bubbles relative to the total area of molten zone, plotted against the post-second peak displacement. Contents of clasts and bubbles were estimated by measuring total areas occupied by them on photomicrographs and BSE images. Data in Figure 2a are shown for comparison without a vertical scale.

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[36] The molten layer contains bubbles of about 50% in volume because bubbles are insoluble into melt due to low-pressure conditions of experiments. Bubbles in the melt tend to lower apparent melt viscosity [e.g., Manga et al., 1998]. We thus corrected apparent viscosity for bubbles using experimental data reported by Lejeune et al. [1999] (open squares in Figure 10a and Table 4), although there is uncertainty in the effect of shape orientation of bubbles and in the interaction between bubbles and clasts in correcting melt viscosity.

Table 4. Summary of Mechanical and Textural Data for Determining Melt Viscosity During Frictional Melting for Six Runs
Run NumberEquivalent velocity, m/sNormal Stress, MPaShear Stress at End of Run, MPaPost-Second-Peak Displacement, mThickness of Molten Layer,a mmApparent Viscosity,b Pa sMatrix Viscosity (Corrected for Bubble),b Pa sMelt Viscosity (Corrected for Clast and Bubble),b Pa sAspect Ratio of ClastClast Content, vol %Bubble Content, vol %
  • a

    Area-averaged thickness. Average effective-thickness shown in parentheses.

  • b

    Viscosity determined using average effective-thickness shown in parentheses.

HVR0140.851.41.25.533 (31)45 (42)81 (75)69 (64)2.063.743.4
HVR0160.851.41.09.284 (74)97 (86)177 (156)150 (132)2.054.153.0
HVR0400.851.40.914.8104 (81)106 (82)194 (150)150 (116)2.056.352.1
HVR0410.851.40.821.0116 (87)108 (81)196 (147)150 (112)2.176.550.6
HVR0430.851.40.836.5108 (82)96 (74)174 (133)80 (61)2.1216.749.3
HVR0120.851.40.860.9135 (122)123 (112)222 (202)74 (67)2.1121.848.2

[37] On the other hand, solid particles in viscous fluid increase its apparent viscosity [e.g., Metzner, 1985], and the effect of clasts can be evaluated using an experimentally derived equation [Kitano et al., 1981]:

  • equation image

with A = 0.54 − 0.0125R, where ηr is the relative viscosity (the ratio of the apparent viscosity of fluid with suspensions to the viscosity of suspending fluid), ϕ is the volume fraction of solid particles, A is a parameter relating to the packing geometry of the solid particle, and R is an average aspect ratio of the solid particles (about 2.0 in our case, see Table 4). Melt viscosity corrected for clasts, using this equation with measured volume fraction and aspect ratio of clasts, is shown with solid diamonds in Figure 10a and is listed in Table 4. Melt viscosity corrected for both clasts and bubbles rises dramatically from about 70 Pa s near the second peak friction up to about 150 Pa s, and the viscosity then gradually decreases to 80 Pa s and stays nearly the same toward the steady state friction.

[38] One problem about the above viscosity estimate is that an area-averaged thickness is used in determining the shear strain rate in Figure 9b. Melting surface becomes very irregular toward the steady state friction (Figures 5c and 5d), and melt pockets in embayed portions, which might have escaped large shearing deformation, are included in the thickness determination. We thus drew straight lines enveloping sticking out portions of host rocks and determined the effective thickness of molten layer by measuring thickness at intervals of 0.4 mm (about 50 measurements in total for each specimen). Melt viscosity was determined exactly in the same manner as for Figure 10a and is shown as open diamonds in Figures 10b. Viscosity thus determined is somewhat smaller than the case using an area-averaged thickness because thinner effective thickness yields greater shear strain rate for a give shear resistance, but the two results exhibit quite similar trends (Figure 10b). These results will give upper and lower bounds of melt viscosity.

4. Discussions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Details
  5. 3. Results
  6. 4. Discussions
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information

[39] We shall now integrate the above mechanical, textural and chemical data to elucidate the physical processes controlling mechanical property of fault during frictional melting. A physical model of frictional melting is proposed at the end that will enable one to model the mechanical properties of faults during frictional melting.

4.1. First Slip Weakening and Subsequent Strengthening on Frictional Melting

[40] The present high-velocity friction experiments on Indian gabbro clearly brought about two stages of potentially unstable, slip-weakening behavior of a fault. Continued slip after the initial static friction causes slip weakening down to the frictional coefficient, μ, of 0.3 to 0.4 over several decimeters of displacement (first slip weakening; Figure 2b). This strength reduction and slip-weakening distance are much larger than those measured in conventional friction experiments with slow slip rates and limited displacements [e.g., Scholz, 1990; Ohnaka, 1992]. Indeed, the slip weakening distance during the first weakening is on the same order as that determined seismologically [Ide and Takeo, 1997; Mikumo et al., 2003; Fukuyama et al., 2003]. The first slip weakening is most likely due to the thermal weakening induced by flash heating at asperity contacts [Rice, 1999]. However, melt patches are already formed on a fault immediately after the first slip weakening (Figures 5a, 5f, and 6a) and temperature along the fault must have exceeded at least melting temperature of biotite (∼650°C). Melting must have gone further than flash heating at asperity tips to form melt patches already at this stage. Our preliminary data clearly shows the weakening distance during the first slip weakening decreases with an increase in the heat production rate, but we shall report on this after conducting more systematic studies.

[41] Tsutsumi and Shimamoto [1996, 1997a, 1997b] have shown experimentally that the onset of frictional melting abruptly increases friction or shear resistance along a fault. The same effect can be seen even more clearly on the frictional coefficient versus displacement curve (point c to d in Figure 2a). Textural observation and mechanical data have revealed that melt patches, with more or less similar geometry, first increases in number and causes rapid strengthening of fault (Figure 8). Melt patches then begin to coalesce and to grow in thickness, and a continuous molten layer forms at around the second peak friction.

[42] Intuitively, one may think that the onset of melting causes marked weakening of a fault, but this is opposite to what is observed. As an example, take a molten layer just after the second peak friction for which an average melt thickness is 33 μm, the average shear strain rate of molten layer is 2.6 × 104 s−1 for the slip rate of 0.85 m s−1, and the apparent viscosity of molten layer is 45 Pa s (Figure 10). This viscosity is rather low as typical of melt with basaltic composition, but the shear resistance of melt is not small owing to extremely large shear strain rate. The shear stress in this case is determined as 1.16 MPa by multiplying the apparent viscosity with the average shear strain rate, and this yields frictional coefficient of 0.83. Thus melt formation is more or less like putting highly viscous material into a fault zone whose dragging effect causes the strengthening. The marked fault strengthening also must have braking effect on seismic fault motion. Rare occurrence of natural pseudotachylytes might imply that the strength increase upon frictional melting acts as a brake to further fault motion, thereby suppressing pseudotachylyte formation.

[43] The logistic curve, equation (3), describes the overall melt growth very well (Figure 7a) and this indicates that the initial increase in average thickness of molten layer is exponential with respect to the displacement after the first peak friction. However, this does not mean that molten layer grows exponentially from a very, very thin molten layer. The initial thicknesses of melt patches are 8 to 10 μm (Figure 8b; see also Figure 6a) although the average initial thickness of melt patches is 2 μm or even less (Figure 9 and Table 2). Thus the initial increase in the average thickness of melt patches (open symbols in Figure 9a) is primarily due to the increase in the number of melt patches.

[44] Thickness of melt patches can dramatically affect the shear resistance of a fault. This can be illustrated by a simple two-dimensional example in Figure 12. Thickness and lateral width of a melt patch with viscosity η are 2H and L, respectively, in Figure 12a, whereas the same amount of melt is thinned to a half of this thickness and elongated twice as wide as this length in Figure 12b. If the slip rate equation image is the same for both cases, the tangential shearing force required to shear the melt patch in Figure 12b is 4 times as large as that in Figure 12a. Initial melt patches occupy about 10% of fault area (Figure 8a). If the same amount of melt is spread over the fault surface, the thickness reduces to about one tenth, and the shear resistance will be about 100 times as large. Of course, such a large resistance is not observed. Shear resistance of infinitely thin molten layer will become infinitely large because shear strain rate (slip rate/melt thickness) becomes infinitely large. However, such an unlikely case is avoided by the formation of melt patches of finite thickness. An increase in the number of melt patches causes strengthening because a fault has to overcome shearing resistance of more viscous melt patches. We do not know at present what determines the initial thicknesses of melt patches, although roughness of fault surface and possibly grain size will play important roles.

image

Figure 12. Schematic diagrams showing (a) a thick melt patch and (b) a thin melt patch with the same area. Tangential shearing forces (shear stress multiplied by the area of molten layer) are given for both cases assuming unit length perpendicular to the figure.

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[45] From present data we do not know exactly how melt patches behaved under extreme shear. The thickness of melt patches is 10 to 20 μm (Figure 8b) and the amount of fault displacement during the melt patch formation causing fault strengthening is on the order of 10 m (Figure 2a), so the shear strain of early melt patches reaches 105 to 106 if they deform uniformly by simple shear. Thus intuitively, one may think that melt patches will be sheared to cover the entire fault surface immediately after their formation. In fact, very, very thin melt patches formed locally, but they do not appear to cover the entire fault surface. On the other hand, wetting angle of molten basalt to a few minerals is measured at 20–50° [Khitarov et al., 1979]. Their basalt has similar chemical compositions to those of our gabbro (compare Table 1 with Khitarov et al.'s Table 1), and hence it is unlikely that melt patches wet fault surfaces in our experiments. Thus another possibility is that melt patches rolled between host rocks more or less maintaining their shapes, just like a mercury drop rolls between two plates moving past each other. Melt patches for which we collected geometrical data in Figure 8b might have behaved like that, but we do not have clear image right now on how melt patches behaved under extreme shear. Systematic work is needed in the future on this.

4.2. Mechanisms for the Second Slip Weakening

[46] The second slip weakening occurs after host rocks are separated by a continuous molten layer, so that the shear resistance of a fault should be determined by the gross viscosity and shear strain rate of the molten layer. Both apparent viscosity of a molten layer and melt viscosity (open circles and solid diamonds, respectively, in Figure 10a) increase sharply at the initial stage of the weakening. Despite this increase in viscosities a fault loses its strength because the molten zone widens and the average shear strain rate sharply drops with increasing displacement (Figure 9b). In other words, the effect of about fivefold reduction in shear strain rate is greater than the effect of about threefold increase in apparent viscosity (compare Figures 9b and 10a). Thus the growth of molten layer is the primary cause of the second slip weakening during frictional melting.

[47] Another important aspect of frictional melting is melt loss from its generation zone into air in experiments (melt splashes from a fault) and into fractures in nature. Melt loss from a simulated fault is unclear soon after the second peak friction is exceeded, but melt splashes become visible under naked eyes as the steady state friction is approached (around point e in Figure 2a). The rate of increase in molten layer thickness declines with increasing displacement during the second slip weakening (Figure 9), so that the melt production should be more or less in balance with melt loss near the steady state friction.

[48] Jaeger [1969, pp. 140–143] solves a simple two-dimensional squeezing problem of a viscous material under a pressure between two plates and shows that the squeezing rate along parallel plates is proportional to the cube of the thickness-width ratio of the material. Although our specimen geometry is different from Jaeger's model, his analysis indicates that melt cannot move much along a fault when a molten layer is very thin, i.e., when marked slip weakening occurs and that melt migration and melt loss become progressively important as a molten layer thickens. Whereas reduction in shear stress and resulting drop in heat production rate should reduce the rate of melting, and a steady state will be attained when the melt production rate is balanced with the rate of melt loss. Melt escaping from the molten zone carries heat away from the molten zone (heat generation zone) and the viscous shear heating can no longer be used all for melt production after the melt loss becomes significant. A complete analysis of frictional melting process should incorporate not only the thickness change of the molten zone, but also the renewed energy budget associated with the melt loss.

4.3. Changing Melt Viscosity: Effect of Temperature or Melt Chemistry?

[49] Melt viscosity notably changes during frictional melting (Figure 10), and we have long thought that this is caused by temperature change in the molten layer, i.e., change in melt temperature due to overshooting of melting temperature as discussed in the next subsection. However, the problem is more complicated because melt chemistry changes during frictional melting (Figure 7) and this can affect melt viscosity as well.

[50] Change in melt chemistry in Figure 7 does appear to reflect selective melting. Percentage of K2O is very high over the whole displacement because minerals with low melting temperature such as biotite, hornblende melted selectively. This is consistent with the absence of biotite and hornblende in the fragments contained in the molten zone. Increasing contents of CaO, Fe2O3, MgO and TiO2 toward the second peak friction (shown as vertical stripe in Figure 7) suggest that clinopyroxene and ilmenite began to fuse toward the second peak friction. This is supported by partially molten clinopyroxene and ilmenite grains with rounded shape recognized after the second peak friction. Percentages of Al2O3 and Na2O first drop and then increase after the second peak friction, which implies that plagioclase (Ab38An62) starts melting early around the second peak friction.

[51] Shaw [1972] proposed a simple, but useful empirical method to predict melt viscosity, including its temperature dependence, from melt chemistry. We calculated melt viscosity at various temperatures for host rock or protolith composition (Table 1) and for melt compositions of 14 specimens with different displacement (Table 3). Calculated viscosities at three temperatures are plotted against displacement in Figure 13a which indicates that viscosity can vary by more than 1 order of magnitude with displacement, reflecting changing chemical composition of melt. The estimated viscosity is high initially and tends to decrease toward the second peak friction, and this is mainly due to the change in SiO2 and Al2O3 contents. Chemical composition and predicted viscosity becomes uniform toward the steady state friction (Figures 7 and 13a).

image

Figure 13. Melt viscosity at different temperatures, as estimated from chemical compositions (Tables 3) using Shaw's [1972] method, plotted (a) against the post-first peak displacement and (b) against the post-second peak displacement. Estimated viscosity for host rock (protolith) is also given at the left end of Figure 13a. Figure 13a also exhibits apparent viscosity, estimated neglecting the effects of bubbles and clasts, for melt patches (open circles; solid-solid frictional coefficient is assumed to be 0.4) and for molten layers (solid circles); see Figures 8c and 10a for original results. Maximum and minimum viscosities for molten layers, collected for bubbles and clasts, are plotted in solid and open diamonds, respectively, in Figure 13b; see Figure 10b for the original results.

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[52] To test whether viscosity changes of melt patches in Figure 8c and those of molten layer in Figure 10 are due to changing melt temperature or due to a change in melt chemistry, we have plotted apparent viscosity of melt patches, assuming solid-solid frictional coefficient is 0.4, in open circles and apparent viscosity of molten layers in solid circles in Figure 13a. Even taking into account the possible ranges of viscosity of melt patches (open circles and open diamonds in Figure 8c), the apparent viscosity notably increases as melt patches develop into molten layers and then it remains nearly constant toward the steady state friction. This initial increase in viscosity is opposite to the trend estimated from melt chemistry and cannot be explained by changing melt chemistry. We believe that the initial low viscosity is due to the high temperature of melt patches created by concentrated shear heating in thin melt patches.

[53] Figure 13b compares melt viscosity corrected for bubbles and clasts (Figure 10b) and viscosity estimated from melt chemistry for 6 specimens exceeding the second peak friction. The melt viscosity increases by about a factor of 2 soon after the second peak friction is exceeded (the first four datum points in Figure 13b). Those points fall roughly along equitemperature lines of around 1100°C, so that the viscosity change could be due to the changes in melt composition, rather than the temperature change in the molten layer. However, this change in viscosity is much smaller than the overall changes shown in Figure 13a. Thus the present data suggest that changes in melt viscosity depends primarily on changing temperature of melt patches and molten layers, but that melt chemistry affects local fluctuation of its viscosity.

[54] We have measured melt temperature of 1140°C at steady state regime using K-type thermocouples and a radiation thermometer, following the same procedures as Tsutsumi and Shimamoto [1997b]. This temperature value is on the same order as that estimated from measured viscosity and Shaw's [1972] method (Figure 13).

4.4. Frictional Melting as a Stefan Problem

[55] On the basis of mechanical and observational data, we now propose a physical model of frictional melting. To state our conclusion first, frictional melting processes can be solved as a class of problems called “Stefan problem” [e.g., Alexiades and Solomon, 1993; Hill, 1987], handling moving boundaries due to melting, freezing and other phase changes [Fialko, 1999; Hirose, 2002]. After host rocks are separated by a continuous molten layer, (1) rock-on-rock friction can no longer be the heat source and viscous shearing of a molten layer becomes the primary heat source after the second peak friction, and (2) viscous shear resistance of the molten layer primarily determines the fault strength during the second slip weakening (Figure 14a). Unlike most melting problems treated in engineering, the heat source is distributed within the molten layer itself in the present case. Accumulation of clasts and bubbles in the molten layer is a complication factor.

image

Figure 14. (a) A schematic diagram showing physical processes involved with frictional melting, and (b) sketches for the melt escape from fault zones (left) for frictional melting experiments and (right)for frictional melting along a natural fault forming pseudotachylyte.

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[56] Melting absorbs heat due to latent heat and hence melting surfaces are big heat sink in the system (Figure 14a). If melting occurs very slowly, excess heat is taken away by latent heat and temperature in the system becomes homogeneous and stays at the melting temperature (equilibrium temperature). However, for rapid phenomena such as seismogenic fault motion, temperature distribution (viscosity distribution) and melting rate are determined dynamically due to the rates of heat generation, heat transfer and melting. The rate of melting or the growth rate of molten layer is determined primarily by the rate of heat transfer to the melting surfaces. If the rate of heat transfer to the melting surface is not rapid enough to take all excess heat away, overshooting of melting temperature within a molten layer will occur. Thus it is not surprising if the change in melt viscosity such as that in Figure 13 is caused by changing melt temperature during frictional melting.

[57] An analysis of heat transfer into melting surfaces and into host rocks from distributed heat sources yields temperature distribution in the system. Temperature distribution within a molten layer in turn determines viscosity distribution in the molten layer, and this viscosity distribution determines the mode of shearing deformation and hence the mode of distributed heat source. Melting does not require nucleation, so that overshooting of melting temperature rarely occurs at melting surfaces [e.g., Alexiades and Solomon, 1993]. It is thus often assumed that temperature stays at melting temperature at melting surfaces (moving boundaries) to solve the coupled problem (often called Stefan condition). Those coupled problem can be solved as a one-dimensional problem. However, when one attempt to compare theoretical prediction with experimental results, it should be kept in mind that frictional melting in laboratory specimens cannot be treated as a one-dimensional problem because heat transfer occurs in three dimension for the specimens (more rapid cooling than predicted by one-dimensional analyses). This effect causes an increase in the slip weakening parameter, dc.

[58] In addition, melt loss has to be incorporated in the analysis and it can also take heat away from melting surface (Figure 14b). Among the coupled processes, melt loss may be hardest to incorporate since melt injection into host rock itself is a complex problem accompanied by cooling and solidification [see Newall and Rast, 1970]. Melt loss in balance with melt production rate should primarily determine a stable thickness of molten layer and the level of steady state friction during frictional melting. Cracks in host rocks may not open under extremely large pressures, as expected at great depths where deep focus earthquakes occur, melt may not be lost from its generation surface causing continued loss of strength. In practice, the effects of melt loss can be examined as two extreme cases; one is “free melt loss” as in our experiments and the other is “no melt loss”. Real cases will fall in between the two.

[59] Significance of melt loss can be recognized in considering the data on the shear stress plotted against normal stress in Figure 4. At a glance, the relationship between the two appears to be a familiar linear relationship for friction, like Byerlee's friction law at high pressures [Byerlee, 1978]. However, the data in Figure 4 are not for solid-solid friction but for a molten layer separating host rocks. The range of normal stress is far too small to expect much effect on viscosity due to the pressure change. Then what is causing the pressure dependence of the shear resistance of the molten layer? It is likely that melt is squeezed more from a fault zone under a higher normal stress, resulting in a thinner molten layer. Then shear strain rate would become higher at a higher normal stress to increase the shear resistance. However, real processes would be more complex since this increase in the shear resistance may cause an increase in melt temperature and a drop in melt viscosity. Our present data are not sufficient to discuss the detailed underlying processes responsible for the normal stress dependence in Figure 4 beyond this rough sketch, and we plan to do a systematic work on this in the future. The effect of normal stress on melt patches formation is also significant. Our experimental results have clearly shown that the friction or shear resistance markedly increases with the formation of melt patches. Whether this strength barrier is indeed as large as that shown in Figure 2 even at great depths with much greater heat production rates must be reexamined based on detailed analyses of the normal stress dependence of frictional melting processes.

[60] Another important problem with respect to earthquake generation is the prediction of slip-weakening parameter, dc. This parameter is almost 10 m for the case in Figure 2a, but dc approaches seismically determined values (typically several decimeters to about 1 m [see Ide and Takeo, 1997; Mikumo et al., 2003; Fukuyama et al., 2003] with increasing slip rates (Figure 3). Higher heat production rate at a higher slip rate must have increased the melt production rate to shorten dc. Thus a big goal of the analyses of the above Stefan problem is to predict dc and the amount of strength reduction that are both critical to the stability analyses of fault motion [e.g., Dieterich, 1978]. Frictional melting is a highly nonlinear phenomenon for which slip history itself determines fault properties. We believe that physical processes during frictional melting are understood reasonably well, and we now throw the ball into the hands of theoreticians and modelers.

5. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Details
  5. 3. Results
  6. 4. Discussions
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information

[61] The major results from present work are as follows:

[62] 1. High-velocity friction experiments on gabbro have revealed two stages of slip weakening; the first weakening is associated with flash heating and incipient formation of melt patches, and the second weakening is associated with frictional melting. The two stages of weakening are separated by a marked strengthening regime that is caused by the growth of melt patches into a thin, continuous molten layer at the second peak friction. Natural pseudotachylytes are associated with the second slip weakening. Initial melting may act as a stopping mechanism for fault slip, and this may be a reason why pseudotachylytes are rare along large-scale faults.

[63] 2. Mechanical properties of faults during frictional melting at depths can be predicted by solving a Stefan problem with moving melting surfaces, combining shearing of molten layer as a heat source, heat transfer with melting, and melt loss into fractures in the host rocks. Rate of melting and the onset of melt loss appear to be the primary processes to determine the slip-weakening parameter dc and the amount of strength reduction. Modeling of initial melting processes (melt patches to molten layer) and analysis of melt-loss processes into fractures in host rock will be difficult tasks for complete modeling of frictional melting processes.

[64] 3. The Dc paradox, or large gap in the slip-weakening distance between the values determined in laboratory friction experiments and seismological analyses, may be solved by considering frictional melting although it is not the only mechanism since pseudotachylytes are not so common along large-scale natural faults. Thermal pressurization [Sibson, 1973; Lachenbruch, 1980; Mase and Smith, 1987] can be an important process that can suppress frictional melting. Frictional heating problem should be solved eventually incorporating fluids in fault zones.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Details
  5. 3. Results
  6. 4. Discussions
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information

[65] We thank A. Tsutsumi, C. A. J. Wibberley, J. Rice, T. E. Tullis, Y. Takei, and K. Mizoguchi for useful discussions and Y. Hayasaka and Y. Shibata for their technical assistance with SEM analysis. We also thank T. Yamashita, J. Spray, and an anonymous reviewer for careful reviews. In particular, the review of an anonymous reviewer tightened up our arguments and clarified a few fundamental points in the frictional melting. This work was partially supported by grants-in-aid for scientific research (12440136 and 16340129) and by a grant-in-aid for the 21st Century COE Program (Kyoto University, G3).

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  5. 3. Results
  6. 4. Discussions
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information
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Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Experimental Details
  5. 3. Results
  6. 4. Discussions
  7. 5. Conclusions
  8. Acknowledgments
  9. References
  10. Supporting Information
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jgrb14210-sup-0001-t01.txtplain text document0KTab-delimited Table 1.
jgrb14210-sup-0002-t02.txtplain text document2KTab-delimited Table 2.
jgrb14210-sup-0003-t03.txtplain text document2KTab-delimited Table 3.
jgrb14210-sup-0004-t04.txtplain text document1KTab-delimited Table 4.

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