Physical state of water controls friction of gabbro-built faults

Domain: earth_science
Published: 2023-08-08
Editorial outcome: minor_revision

Abstract
Earthquakes often occur along faults in the presence of hot, pressurized water. Here we exploit a new experimental device to study friction in gabbro faults with water in vapor, liquid and supercritical states (water temperature and pressure up to 400 °C and 30 MPa, respectively). The experimental faults are sheared over slip velocities from 1 μm/s to 100 mm/s and slip distances up to 3 m (seismic deformation conditions). Here, we show with water in the vapor state, fault friction decreases with increasing slip distance and velocity. However, when water is in the liquid or supercritical state, friction decreases with slip distance, regardless of slip velocity. We propose that the formation of weak minerals, the chemical bonding properties of water and (elasto) hydrodynamic lubrication may explain the weakening behavior of the experimental faults. In nature, the transition of water from liquid or supercritical to vapor state can cause an abrupt increase in fault friction that can stop or delay the nucleation phase of an earthquake.

Introduction
Seismological, geophysical, and deep borehole data plus field observations of exhumed faults are consistent with the hypothesis that crustal earthquakes often originate and propagate in the presence of hot and pressurized (i.e., hydrothermal) fluids1–3. Moreover, experimental studies indicate that hydrothermal fluids (usually water) govern the seismic cycle by means of a plethora of physical and chemical processes4–7 (pore pressure variations, diffusive mass transfer, mineral precipitation, sub-critical crack growth, etc.), which determine, for instance, fault frictional instability or its healing and sealing. However, the role of the physical state (liquid, vapor, and supercritical) of water in the seismic cycle remains unclear, especially in relation to the safe exploitation of deep geothermal reservoirs8. Rock friction experiments performed over a broad range of slip distances (up to meters) and slip velocities (from a few μm/s, or sub-seismic, to m/s, or seismic) can contribute to the understanding of the seismic cycle9–19. So far, because of technical challenges, rock friction experiments15,16,20–25 under hydrothermal conditions have been limited to low slip velocities (≤ ~100 μm/s) and short slip distances (≤ ~80 mm). As a consequence, the frictional properties of fault rocks at seismogenic conditions in the presence of water under different physical states are still poorly understood.

Here we exploit a new experimental setup to investigate the effect of the physical state of water on fault friction in the seismic cycle. In the case of gabbro, a common crustal rock, liquid (but at high temperature and pressure) and supercritical water result in a large decrease in fault friction regardless of the imposed fault slip velocity, while in the case of vapor fault friction decreases with slip velocity. We propose three possible mechanisms which may contribute to the reduction of fault friction during shear: (1) the formation of clay minerals along slickensides due to water-rock interaction; (2) the H–O–H bonding properties of water at hydrothermal conditions; (3) viscous “slurry-like” lubrication due to the presence of water and rock powders produced during slip.

Results
Experimental protocol
We performed 25 rock friction experiments on cylindrical samples (28 mm external diameter) of gabbro in a rotary shear machine26 equipped with an on-purpose designed hydrothermal vessel (for details on experimental setup, rock composition, list of experiments and data reproducibility see “Methods”, Supplementary Figs. 1–3 and Supplementary Tables 1, 2). Two gabbro cylinders were sheared for slip distances up to 3 m at constant sub-seismic to seismic slip velocities (V from 1 μm/s to 0.1 m/s) under drained “hydrothermal conditions” in the presence of pressurized distilled water in liquid (temperature T=300 °C, pore fluid pressure P f=10 MPa), vapor (T=400 °C, P f=10 MPa) and supercritical (T=400 °C, P f=30 MPa) states. In all the experiments the imposed effective normal stress (σ n eff=σ n –αP f assuming α=1, where σ n is normal stress) was 10 MPa. Fault strength is reported as friction coefficient μ=τ/σ n eff, where τ is shear stress. The samples were recovered after the experiments for microanalysis (see “Methods”) with Field Emission Gun Scanning Electron Microscope (FESEM), X-Ray powder diffraction (XRPD), Micro-Raman spectroscopy, and non-contact optical profilometer (OP) techniques.

Mechanical results
In the experiments, the friction coefficient of gabbro evolved with slip distance, slip velocity and physical state of water as follows (Fig. 1):

Water in the liquid state. Regardless of the imposed slip velocity, slip-weakening behavior was observed. The friction coefficient of gabbro increased over a slip distance of 10–30 mm from an initial static friction coefficient μ s = 0.61–0.80 to the peak one μ p = 0.75 ± 0.10, and then decayed over a slip distance of ~200–500 mm to the steady-state μ ss = 0.20–0.35 (Fig. 1a). Despite the similar trends of slip-weakening, the values of μ s, μ p and μ ss, though with some scatter, decreased with increasing slip velocity (Fig. 1b).

Water in the supercritical state. Regardless of the imposed slip velocity and similar to experiments performed with water in the liquid state, the friction coefficient of gabbro increased over a slip distance of 10–280 mm from μ s = 0.5–0.58 to μ p = 0.6 ± 0.10, and then decayed over a slip distance of ~300–500 mm to μ ss = 0.2–0.3 (Fig. 1c). The μ s, μ p, and μ ss values were almost independent of slip velocity (Fig. 1d).

Water in the vapor state. Differently from the experiments with water in liquid and supercritical states, the friction behavior of gabbro was velocity-dependent (Fig. 1e). In particular, for 0.01 ≤ V ≤ 1 mm/s, the friction coefficient remained high: from μ s = 0.75 ± 0.05 it increased to μ p = 0.81–0.92 and then decreased to μ ss = 0.67–0.72 (Fig. 1f). Instead, for V = 10 mm/s, the friction increased from μ s = 0.51 to μ p = 0.66 and then first decayed to 0.47 ± 0.05 over a slip distance of ~200 mm and then further decreased to 0.2 till the end of slip. At V = 100 mm/s, the friction coefficient decayed from μ s = 0.57 and μ p = 0.64 to μ ss = 0.26 after ca. 250 mm of slip. The μ s, μ p and μ ss values evolved from velocity-neutral to velocity weakening with increasing slip velocity (Fig. 1f).

The mechanical data show that the physical state of water impacts the friction properties of the experimental fault to a much greater extent than previously thought. For instance, in experiments performed with tri-axial machines (i.e., slip distance < 1 mm, slip velocity < 0.1 μm/s) on quartz gouges, the decrease of friction coefficient at the water transition from the liquid to the vapor state was limited to ~0.0527. Instead, we measured an increase in friction coefficient at this transition for larger slip distances and velocities (Fig. 1b, f).

Micro-analytical results
To identify the possible deformation mechanisms responsible for these large measured differences in the frictional behavior of gabbro rocks, the samples were recovered for mineralogical and microstructural investigations. Unfortunately, part of the non-cohesive powder produced during shearing in the slip zone might have been flushed away during fluid ejection and sample unloading. However, regardless of the imposed slip velocity, the slip surfaces of the faults that were whitish in color before the experiments acquired a dark green color in the experiments with liquid and supercritical water and medium green color in the experiments with water in the vapor state (left panel of Fig. 2a–c). After the experiments, the slip surfaces were ultra-polished and lineated (i.e., striae parallel to the slip vector, see Supplementary Fig. 4) and, based on optical profilometer measurements, had a micro-roughness with a root mean square (RMS) of ~3.5–7 μm (middle panel in Fig. 2a–c) (for starting surface see Supplementary Fig. 5). The slip zones beneath the slip surfaces were <30 μm thick (inset in Fig. 2b for the experiment performed with supercritical state water) and made of ultra-fine powders with grain size down to few nm (right panel in Fig. 2a–c). In particular, the powders from the experiments conducted with water in the supercritical state included ultra-fine (∼200 nm long and ∼30 nm thick) newly formed clay-like minerals (yellow arrow in the right panel of Fig. 2b). However, their size was too small for FESEM-elemental analysis. XRPD analysis performed directly on the slip surfaces (Fig. 2d) and on the powders (~10 mg, after ethylene glycol treatment, Supplementary Fig. 6) recovered from the slip zone revealed the presence of a broad peak at 8° in the spectra of the gabbro sheared with water in the liquid or supercritical state. This broad peak, typical of smectite and chlorite28, was absent in the XRD spectra of the surfaces of the starting (not sheared) gabbro and of the slip surfaces recovered after the experiments with water in the vapor state. Based on XRD semi-quantitative analysis, the abundance of these newly formed minerals is estimated to be less than 5 wt.%. Similarly, a peak at a wavenumber of 1595–1600 cm−1 was present only in the micro-Raman spectra of the ultra-polished slip surfaces recovered from the experiments performed with water in the liquid and supercritical states (Fig. 2e). This wavenumber corresponds to the H–O–H bending vibrational mode of H2O29 and is possibly associated with the water absorbed in the slip surfaces or immediately beneath (the micro-Raman exciting signal can penetrate <1 μm). In the micro-Raman spectra map (600 × 600 μm2) of the slip surfaces, the signal of the H–O–H bending overlaps with the location of the striae (Fig. 2f and Supplementary Fig. 7). This implies that the formation of this particular H-O-H bond is associated with the development of high-strain zones.

In conclusion, the microstructural and microanalytical analysis confirm the formation of an ultra-polished slip surface topping a few tens of micrometers (inset in Fig. 2b) thick slip zone in all the experiments. However, only in the experiments performed with liquid or supercritical water (i.e., when, regardless of the imposed slip velocities, the lowest values of the friction coefficient were measured; Fig. 1) the slip zone is enriched in H–O–H bonds water and includes newly-formed water-bearing minerals (Fig. 2).

Methods
Friction experiments
The experiments were performed in a Low to High-Velocity rotary shear machine, located at the State Key Laboratory of Earthquake Dynamics at Institute of Geology, China Earthquake Administration (IGCEA)26, equipped with a dedicated hydrothermal pressure vessel. More detailed descriptions are shown in Supplementary Fig. 1. The rock used for friction experiments was gabbro named “Jinan dark green”. Mineralogical composition could be found in Supplementary Tables 1, 2. The samples for experiments were machined into cylinders of 28 mm in diameter and 25 ± 1 mm in height. Two parallel grooves of 12 mm in length and 3 mm in width at the base of samples were carved on both sides to fit with the sample holder. Samples were jacketed with Nickel-made rings rather than Aluminum-made rings, commonly used for room-temperature experiments, to avoid rock failure during the shearing. On both upper and lower columns, graphite rings of ~20 μm diameter smaller than the internal diameter of the chamber were used as adjusters for better alignment of the columns.

The experiments were all performed under drained conditions (ISCO syringe pump maintained the system at a constant pore pressure). An effective normal stress of 10 MPa was imposed to the rock and remained constant throughout each experiment. The temperature was measured with a thermocouple located approximately at the center of the rock cylinder and ~1 mm away from the slip surface.

The experimental sequence was:
(1) pre-grinding process was conducted at 2 cm/s, under 0.5 MPa normal stress to reduce the misalignment of rock surfaces until the oscillation of axial displacement in one revolution is less than 5 μm;
(2) powders produced on the sliding surfaces were removed by using pressurized air and ethanol-wetted papers;
(3) the sample assemblage was re-mounted into the machine;
(4) the vessel was vacuumed to 2000 Pa;
(5) water was injected into the vessel and the pore pressure increased to the target value;
(6) the normal stress was loaded to the target value;
(7) the vessel was heated with the external furnace and the pore pressure was kept at a constant value (the amplitude of the pressure oscillation was less than 0.5%, see Supplementary Fig. 2a);
(8) once the desired temperature was achieved (this took 1-2 h, Stage 1, Supplementary Fig. 2a), samples were sheared at a constant velocity spanning from 1 μm/s to 0.1 m/s for a slip distance up to 3 m (slip distance, slip velocity and shear stress were determined using the methods outlined in Ref. 6) (Stage 2, Supplementary Figs. 2a, b). Normal load was measured with a load cell with a resolution of 10 N. Shear torque was recorded by the cantilever-type torque gauge consisting of a horizontal arm and a pair of force gauges with a resolution of 0.01 Nm. Axial displacement (i.e., sample plus loading column) was measured by a linear variable differential transducer (LVDT) with a resolution of 1 μm. The angular velocity and rotary angle were recorded with an encoder and a high-precision potentiometer, respectively. Pore pressure was measured by a pressure transducer (100 MPa full range with 0.01 MPa resolution) positioned between the outlet of the syringe pump and the inlet of the vessel. The temperature was measured by a K-type thermocouple (resolution 0.1 °C) placed ~1 mm away from the slip surface. All parameters were acquired at a frequency up to 1 kHz. When the target slip distance was achieved, we stopped the motor and turned off the furnace. The cooling process to room temperature lasted about 2 h (Stage 3, Supplementary Fig. 2a);
(9) the samples were recovered from the vessel chamber and prepared for micro-analyses.

Fault strength was presented as friction coefficient μ, the ratio of measured shear stress to effective normal stress. For each experiment, the static friction coefficient (μ s) or the friction coefficient value when sliding starts on the fault, and peak friction coefficient (μ p) were obtained from the curve of friction coefficient with time (Supplementary Fig. 2). We determined the steady-state friction coefficient (μ ss) as the average value within a distance window of ~200 mm which covers ~4 rotations of the cylindrical samples to minimize the effects of the frictional fluctuations due to the rotary configuration (see Supplementary Table 1 and Supplementary Fig. 2). Correspondingly, the shortening (or dilatancy) rate at steady-state was calculated as the ratio of axial displacement to slip distance over the same slip distance range. To assess the effect of the physical state of water on fault friction, experiments with liquid, vapor and supercritical water were performed under otherwise identical loading conditions. Although the final slip distance is relatively small in the experiments performed at V ≤ 0.1 mm/s, it is worth noting that, the evolution of fault friction is remarkably different depending on the physical state of water.

Modeling of the temperature increase in the slipping zone
The temperature increase due to shear heating was estimated as first-order using a coupled Finite Element Analysis 2‐Dimensional time-dependent model in Matlab®. In this model, we computed the heat source and heat dissipation in time and space. We considered a 2‐D sample (28 × 25 mm, or the diameter versus height of each cylinder of gabbro) bounding the water-saturated slip zone. The initial effective normal stress was equal to the one imposed in the experiments. Fluid thermal and physical (e.g., thermal conductivity, density, compressibility) properties were taken from NIST database as a function of temperature T and fluid pressure P imposed during the experiments (e.g., vapor, supercritical and liquid states; see Supplementary Table 3). Two different materials were used to simulate the experimental slip zone and the wall rock (gabbro). The wall rock was regarded as very low porous media, whereas the initial porosity of the slip zone was ϕ = 1 − A r/A = 0.95, where A r is the real contact area and A is the nominal area of the slip surface. The slipping zone has a width of 100 μm. The thermal and hydraulic properties of the slipping zone were k eff=(1−ϕ)×k r+ϕ×k f and ρC eff=ρ r×C r×(1−ϕ)+ρ f×C f×ϕ, where the subscripts r and f are related to the rock and fluid properties, respectively. The fluids and rock properties were considered constant during the modeled experiments. In the model, the experimental fault is sheared at the imposed slip velocity V(t, r). We assumed that all the mechanical energy is dissipated as heat54,55 (possibly overestimate), so the heat flux Q(r, t) = 0.5 · τ(t) · V(r, t) is a function of time t and the radial distance r from the center of the sample. A Neumann boundary condition was applied to the bottom external edge (i.e., slip zone) of the model to consider the flux of heat due to shearing. On the other three external boundaries, a constant temperature T=T 0 as the initial experimental temperature of the two materials and a constant fluid pressure P f=P 0 function of the experimental conditions (Supplementary Table 3) for the slipping zone were imposed. At the inner boundary between the slip zone and the wall rock, the continuity of the solution was granted.

Elastohydrodynamic (EHD) lubrication
EHD was proposed to explain the reduction in friction during seismic slip when viscous fluids are present between rough surfaces of tectonic faults46. Following Eq. (1), the Sommerfeld number S controls the transition from boundary lubrication (solid-solid contacts) to mixed lubrication (mixed contacts) to full hydrodynamic lubrication (interstitial fluid film). In the case of vapor condition (T=400 °C, P f=10 MPa) in our experiments, η H2O = 2.5 × 10−5 Pas, the rock surface at the end of the experiment has a roughness of RMS ~3.5 μm. The perimeter of our sample (88 mm) is considered as the characteristic length L. For activation of S ≥ 0.001, the required slip velocity is roughly estimated to be higher than 10 mm/s.

X-Ray powder diffraction
X-ray powder diffraction (XRPD) measurements were performed at the Department of Geoscience at the University of Padova using a Philips X’Pert Pro MPD diffractometer. The instrument is equipped with a long-fine-focus cobalt anode tube working at 40 kV–40 mA and a 240 mm goniometer radius that operates in the θ/θ geometry. Incident beam optics include the Bragg–Brentano HD (BBHD) module: a wafer crystal of W/Si manufactured to improve signal-to-noise and peak-to-background ratios while maintaining a divergent beam and reducing Kα-2 and Kβ lines. Divergence slits of ¼°, antiscatter slits of 1° and Soller slits of 0.04 rad complete the incident beam setup. Diffracted beam optics are composed of antiscatter slit of 9.1 mm aperture, Soller slits of 0.04 rad and X’Celerator Position Sensitive Detector with a 2.122° 2θ active length.

Measurements for phase identification were carried out between 3° and 85° 2θ angle, using a 0.017° step size, counting 100 s per virtual step on a spinning sample (1 revolution per second): total scan time is 1 h and 6 min. Samples were prepared using the front-loading procedure onto a Si-crystal sample holder produced to have no diffraction lines (zero-background) suitable for the small amount of material available. Oriented and Ethylene glycol saturated samples were measured between 2.5° and 42° 2θ angle, using a 0.033° step size, counting 200 s per virtual step.

Mineralogical species in bulk samples were identified using the search and match procedure implemented in PANalytical HighScore Plus v. 4.9.0 (Malvern Panalytical Ltd, Malvern, UK). Phyllosilicates and clay groups were recognized29.

Micro-Raman spectroscopy
Raman spectra were collected at the Department of Geoscience at the University of Padova, using WITec Alpha R confocal microscope with a XYZ motorized stage and equipped with the 532 nm laser diode (maximum power: 60 mW) and with a 300 lines/mm grating that ensures a ~2 cm−1 resolution over a spectral range from 0 to 4000 cm−1. Raman spectra were recorded with an integration time of 0.25/0.5 s and for each spectrum, 30 scans were accumulated. The applied power ranges from 5 to 10 mW.

Non-contact optical profilometer
The surface morphometrics was performed at the Department of Geoscience at the University of Padova with a portable non-contact 3D optical profilometer Nanovea Jr25, equipped with an optical pen providing a vertical resolution (height repeatability) of 3.4 nm. The measurements were done on 2 × 2 mm2 areas, using a lateral resolution (step size) of 2 μm and a scan speed of 4 mm/s (2000 Hz). The 3D maps were processed with the software Gwyddion v2.61 (Czech Metrology Institute). The final calculation (selected 1 × 1 mm2) of the texture parameters, including those from the standard EN ISO 25178-2, was performed by a 3D analysis of the height maps including the high-pass roughness component and the low-pass waviness component together (that is, no wavelength cut-off was set).

Field emission gun scanning electron microscope
SEM images were collected on a Tescan Solaris Field-Emission SEM at the Department of Geoscience at the University of Padova. Images have been acquired with an in-beam mid-angle backscattered detector using an accelerating voltage of 5 KeV, current of 300 pA and a working distance of 3 or 4 mm.

Data availability
The experiment data files used in this study are available at https://zenodo.org/record/7520657.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript by Wei Feng and co-authors presents laboratory-derived evidence of fault weakening that appears to be controlled by the phase of water present at the frictional interface. With the help of a new hydrothermal rotary shear apparatus, the authors have probed a previously unexplored combination of controlled parameters:\n1. sliding velocities spanning 5 decades, ranging from nucleation up to intermediate sub-seismic values,\n2. large slip distances, and\n3. water in liquid, vapor, or supercritical form.\nThe authors argue that previously documented mechanisms, i.e., dynamic weakening and strain localization in shear bands composed of aligned phyllosilicate minerals, are insufficient to explain the results of their experiments. Instead, based on the mechanical data from the experiments as well as extensive post-mortem analyses of the gabbro specimens, the authors propose two possible weakening mechanisms:\n1. a chemistry-driven mechanism, whereby water in liquid or supercritical state weakens the gabbro interfaces to produce gouge consisting of weakly-bonded phyllosilicate minerals, and\n2. a mechanical/physical mechanism, whereby the mixing of gouge particles with water produces a lubricant of appropriate viscosity to cause macroscopic weakening of the frictional interface.\nA couple of limitations of the study, that, in my opinion, do not weaken its key conclusions, are:\n1. The comparatively small total displacement in some of the experiments with the lowest sliding velocities, which may have prevented the system from reaching its steady-state. However, it is understandable that at such slow sliding velocities, reaching large displacements would require a significant amount of time.\n2. For the modelling of temperature jumps, the assumption that all the mechanical energy is converted into heat is problematic, as there is evidence of gouge production in the experiments. In light of this fact, should the results of the modelling (Supplementary Figure 7) be treated as an \"overestimation\"?\nThe main contribution of this study is that it highlights the role of water's physical state in enabling the operation of the proposed weakening mechanisms. I believe that the explanation of the first (chemical) weakening mechanism could be improved by highlighting the contrast with already established mechanisms mentioned earlier in the discussion (also given the unfortunate fact that the produced gouge could not be fully recovered post-mortem). Overall, I recommend the publication of the manuscript with minor modifications/clarifications to address that issue as well as some points mentioned below.\n== Specific comments ==\nLines 16, 17 (Abstract) and 62, 64 (Results): it seems to me that the two sentences are somewhat contradictory regarding the role of velocity in the case of water in the liquid state. According to Figure 1, panels a & b, there is certainly weakening, although a trend with velocity may be difficult to discern (especially if the mu_ss values for the lowest sliding velocities do not capture the true steady-state).\nLine 163: Omit the dash in \"a-dimensional\" (or replace the entire term with \"dimensionless\"?)\nLine 305: Replace \"were\" with \"are\"?\nLine 330: replace \"takes\" with \"took\" to keep the style consist with line 336 (\"lasted\")?\nFigure 1: It would be helpful if the colors of the markers in panels b, d, and f be kept consistent with the colors of the corresponding experiments in panels a, c, and e. Having them in a different color for each water state does not seem to serve any purpose.\nFigure 4: Panel b could benefit from some light reworking. For example the background of the lower inset (\"water layer\") could be made opaque and light blue.", "reviewer_2": "This paper presents new laboratory data on frictional behavior of simulated gabbro faults over a broad range of slip velocities to meter-scale slip distances, systematically contrasting the distinct responses associated with fluid in the forms of water in vapor, liquid and supercritical states. The data are of high quality, and they fill in a critical gap in our understanding of the coupling of phase transition of the saturating fluid and its potential subtle impacts on fault strength and stability. Plausible mechanisms related to water-rock interaction and elastohydrodynamic lubrication are proposed herein to interpret the experimental data. Both methodology and results are presented in details. My primary comments are on certain technical aspects and the Discussion.\nOn the numerical modeling, although the exact width may not impact the final results, the authors should specify what the width of the water-saturated slip zone was in their simulations.\nL161 “However, further studies are required to quantify the role of chemical bonds of absorbed water in fault slip zones” – exactly what types of studies do the authors envision that can clarify this subtle process?\nL171-174 “These estimated viscosities are in the range of those attained by a mixture or suspension of rock powders with water in liquid and supercritical states….” citing references 42 & 43” – the narrative here is misleading and seems to imply that there exist directly relevant measurements on these plausible values. The wording needs to be cleaned up to explicitly provide the logical argument.\nL 304 L332-333 In which lab were these experiments conducted? Although they may have been presented in earlier publications, relevant technical details on accuracy and precision of measurements including slip distance, velocity, stresses, torque, pressure and temperature should also be provided here.\nTypos:\nL27 “faults”\nL41 “is” -> are\nL46 “for” -> For\nL78 “much extent”\nL163 “a-dimensional” -> “adimensional” or “nondimensional”", "reviewer_3": "This manuscript presents results of experimental measurements of frictional properties of gabbro at high-temperature hydrothermal conditions. The authors used a confined rotary shear apparatus to investigate how friction evolves as a function of slip and slip rate, specifically focusing on the state of aqueous pore fluid. The authors conducted experiments spanning 3 possible states of interstitial water: liquid, steam, and supercritical fluid. This is important because transitions between the states may significantly affect the fluid properties, solid-fluid interactions, and frictional strength. Such transitions can occur both as a function of depth, and as a function of slip rate when coseismic heating may substantially modify the local temperature on a slip interface. The authors find that the fluid state indeed controls the frictional properties of gabbro: for liquid water, friction is both slip and velocity weakening, while for steam (vapor) and supercritical state, friction is nearly velocity-neutral (but still slip-weakening). The authors attribute such different behaviors in part to formation of clay minerals, which they verified using a post-experiment microscopy analysis. The presented results are new and warrant publication in Nature Communications. Overall, the manuscript is well written and logically organized. The experimental procedures are well documented, and the methods are state of the art. The results should be of interest to a broad readership, including, but not limited to, experimentalists, seismologists, modelers, and field geologists. I recommend that this manuscript is published, pending a moderate review to address several comments, as described below.\n1) While the experimental part of the study is robust, I am less convinced by the interpretation that appeals to the elasto-hydro-dynamic lubrication (EHDL) mechanism. For this mechanism to work, the fluid has to be essentially incompressible. The latter condition applies to water in a common liquid state, but not to water vapor or supercritical fluid, both of which are highly compressible, and therefore would not be very efficient at \"flattening\" the slip interface by elastic deformation. Between the three fluid stated, the EHDL would be most efficient in case of liquid water; however, the experiments show that in this case the residual dynamic strength is nearly independent of the slip rate (Fig. 1a,b). Based on these arguments, the EHDL is an unlikely mechanism responsible for the observed variations in dynamic friction.\n2) The authors do not mention thermal pressurization as a possible mechanism. Is this because the slip rates are too low to cause a large enough temperature increase? Please elaborate. (The argument about fluid compressibility raised above would also apply in case of thermal pressurization.)\n3) All of the presented experiments exhibit evolution of friction from \"peak\" to \"steady state\" over a characteristic distance of the order of 1 m (Fig.1 a,c,e). A similar evolution (although of smaller magnitude) was reported in rotary shear experiments on dry gabbro (e.g., www.nature.com/articles/nature11370). Could there be a common mechanism, possibly enhanced by the presence of fluid? Please discuss.\n4) line 35. Instead of \"at seismic deformation conditions\", consider \"at seismic slip rates\", or \"at seismogenic conditions\".\n5) line 78. \"to a much extent\" -> \"to a much greater extent\".\n6) line 90. \"After the experiments, the slip surfaces were ultra-polished and lineated\" - it would help to include a figure illustrating this, perhaps in Supplementary Materials."}, "author_response": "Response to reviewers’ comments\nWe would like to thank all three reviewers for their constructive comments on our\nmanuscript titled “Physical state of water controls friction of gabbro-built faults”. The\nmanuscript has been modified and significantly improved by their insightful\nsuggestions. Below, you will find our point-by-point response (blue fonts) to the\nreviewers’ comments (black fonts). Line numbers refer to those in the revised version\nof the manuscript.\nReviewer #1 (Remarks to the Author):\nThe manuscript by Wei Feng and co-authors presents laboratory-derived evidence of\nfault weakening that appears to be controlled by the phase of water present at the\nfrictional interface. With the help of a new hydrothermal rotary shear apparatus, the\nauthors have probed a previously unexplored combination of controlled parameters:\n1. sliding velocities spanning 5 decades, ranging from nucleation up to intermediate\nsub-seismic values,\n2. large slip distances, and\n3. water in liquid, vapor, or supercritical form.\nThe authors argue that previously documented mechanisms, i.e., dynamic weakening\nand strain localization in shear bands composed of aligned phyllosilicate minerals, are\ninsufficient to explain the results of their experiments. Instead, based on the mechanical\ndata from the experiments as well as extensive post-mortem analyses of the gabbro\nspecimens, the authors propose two possible weakening mechanisms:\n1. a chemistry-driven mechanism, whereby water in liquid or supercritical state\nweakens the gabbro interfaces to produce gouge consisting of weakly-bonded\nphyllosilicate minerals, and\n2. a mechanical/physical mechanism, whereby the mixing of gouge particles with water\nproduces a lubricant of appropriate viscosity to cause macroscopic weakening of the\n1\nfrictional interface.\nA couple of limitations of the study, that, in my opinion, do not weaken its key\nconclusions, are:\n1. The comparatively small total displacement in some of the experiments with the\nlowest sliding velocities, which may have prevented the system from reaching its\nsteady-state. However, it is understandable that at such slow sliding velocities, reaching\nlarge displacements would require a significant amount of time.\n2. For the modelling of temperature jumps, the assumption that all the mechanical\nenergy is converted into heat is problematic, as there is evidence of gouge production\nin the experiments. In light of this fact, should the results of the modelling\n(Supplementary Figure 7) be treated as an \"overestimation\"?\nThe main contribution of this study is that it highlights the role of water's physical state\nin enabling the operation of the proposed weakening mechanisms. I believe that the\nexplanation of the first (chemical) weakening mechanism could be improved by\nhighlighting the contrast with already established mechanisms mentioned earlier in the\ndiscussion (also given the unfortunate fact that the produced gouge could not be fully\nrecovered post-mortem). Overall, I recommend the publication of the manuscript with\nminor modifications/clarifications to address that issue as well as some points\nmentioned below.\nWe are grateful to the reviewer for the positive comments on our manuscript, and also\nfor appreciating the importance of our work. We give our response to the comments\nbelow.\nThe reviewer highlighted that:\n“The comparatively small total displacement in some of the experiments with the\nlowest sliding velocities, which may have prevented the system from reaching its steady-\nstate. However, it is understandable that at such slow sliding velocities, reaching large\ndisplacements would require a significant amount of time.”\nthe experiments performed at a low slip velocity (e.g., 83.3 hours for V = 10 μm/s) can\nbe quite time-consuming. However, the primary reason for not performing these long-\nlasting experiments is related to safety concerns: although the cooling system of the\nvessel is quite efficient, extended durations of such experiments could potentially lead\nto hazardous overheating. We are currently working in order to reduce this hazard. In\nany case, the fault friction indeed did not reach a steady-state value in the experiments\nperformed at V≤ 0.1 mm/s. It is important to note that, the mechanical data collected\nfor the shorter but identical slip displacements of 0.3 m and 1 m for V= 0.01 mm/s and\n0.1 mm/s, respectively, still provide useful information about the effects of the physical\nstates of water on fault friction at these low slip velocities. As a consequence, the\nrelatively small displacements imposed in the low velocity experiments do not weaken\nthe main conclusions of our study. To address this point, we now added the following\nstatement in the Methods section (Lines 417-421):\n“To assess the effect of the physical state of water on fault friction, experiments with\nliquid, vapor and supercritical water were performed under otherwise identical loading\nconditions. Although the final slip distance is relatively small in the experiments\nperformed at V≤ 0.1 mm/s, it is worth noting that, the evolution of fault friction is\nremarkably different depending on the physical state of water.”\nRegarding the numerical modeling of temperature rise, we agree with the reviewer that\nour results may not be accurate if we assume all mechanical energy is converted to heat.\nHowever, this assumption has been widely used in previous studies, and justified by the\ngood agreement between the temperature estimated with this hypothesis and the\ntemperature measured by thermocouples at the given locations (Kitajima et al., 2010;\nHan et al., 2011; Yao et al., 2013; 2016; Cornelio et al., 2019). Moreover, Aretusini et\nal., 2021 demonstrated that, at least for a similar experimental configuration (solid rock\ncylinders), almost all the energy dissipated during high velocity friction experiments is\nconverted into heat. With regard to the energy sink associated with gouge production,\nprevious work suggested that the energy consumed by grain crushing and comminution\n3\nonly accounts for a small fraction of the frictional work (0.02%~1.06 % as indicated by\nBET surface area measurements of quartz grains before and after high-velocity friction\nexperiments; Togo and Shimamoto, 2012). It is clear that gouge production is a\nrelatively small energy sink. Additionally, there are a few more factors, such as the\nwidth of the slipping zone and the heat convection of the fluid, that may affect the\nestimated temperature rise. To avoid adding the complex discussion above in the main\ntext, we simply cited several references to support this assumption of heat source (ref.\nnumber 54, 55; line 438) and stated that the temperature modeling results are first-order\nestimates (and possibly overestimate) of the temperature increase in the slipping zone\n(line 423 and line).\nI believe that the explanation of the first (chemical) weakening mechanism could be\nimproved by highlighting the contrast with already established mechanisms mentioned\nearlier in the discussion.\nMoreover, in the Discussion section about the possible “chemical” weakening\nmechanism, we have made slight adjustments to the sentence structure to enhance\nlogical flow. We also highlighted the distinctiveness of the “chemical” weakening\nmechanism proposed, and specified that understanding the microstructure and\ndynamics of hydrogen bonds in future studies may be useful to clarify this “chemical”\nweakening mechanism (Lines 181-184).\n“This possible weakening associated with the chemical bonds of absorbed water is\nquite different from the established weakening mechanisms. Further studies on the\nmicrostructure and dynamics of hydrogen bonds are required to quantify the role of\nabsorbed water in affecting the frictional behavior of fault zones.”\n== Specific comments ==\nLines 16, 17 (Abstract) and 62, 64 (Results): it seems to me that the two sentences are\n4\nsomewhat contradictory regarding the role of velocity in the case of water in the liquid\nstate. According to Figure 1, panels a & b, there is certainly weakening, although a trend\nwith velocity may be difficult to discern (especially if the mu_ss values for the lowest\nsliding velocities do not capture the true steady-state).\nWe thank the reviewer for pointing out these unclear descriptions. In the abstract (now\nLines 17-18), we aim to highlight that the slip-weakening behavior (i.e., friction\ndecreases with slip distance) is independent of slip velocity, rather than the dependence\nof friction coefficient on the imposed slip velocity. Furthermore, in the results (now\nLines 61-67), we describe that these friction parameters (i.e., µ,µ andµ values) have\ns p ss\na slight tendency to decrease with increasing slip velocity. They are actually the\ndifferent observations. Following the comments of the reviewer, and to avoid confusing\nthe reader, we now added additional text at lines 64 and 67:\n“Regardless of the imposed slip velocity, slip-weakening behavior was observed.”\n“Despite the similar trends of slip weakening, the values of µ,µ andµ , though with\ns p ss\nsome scatter, decreased with increasing slip velocity.”\nLine 163: Omit the dash in \"a-dimensional\" (or replace the entire term with\n\"dimensionless\"?)\nChange made.\nLine 305: Replace \"were\" with \"are\"?\nThanks, “were” has been replaced with “are”.\nLine 330: replace \"takes\" with \"took\" to keep the style consist with line 336 (\"lasted\")?\nThanks, it has now been corrected.\nFigure 1: It would be helpful if the colors of the markers in panels b, d, and f be kept\nconsistent with the colors of the corresponding experiments in panels a, c, and e. Having\nthem in a different color for each water state does not seem to serve any purpose.\nWe thank the reviewer for the suggestions on Figure 1 and we do agree that Figure 1\n5\nwould be improved if the colors of the slip velocity markers are kept consistent in the\nleft and right panels. At the same time, we would also like to keep the consistency of\n“blue in color = liquid water; green in color = vapor water; red in color = supercritical\nwater” in Figures 1 and 2 for all the plotted curves and symbols for data obtained from\nfriction experiments and various analysis. Taking into account the reviewers’ comments\nand our concerns, we have decided to modify Figure 1 as shown below (see Updated\nFigure 1).\nUpdated Figure 1\nFigure 4: Panel b could benefit from some light reworking. For example the background\nof the lower inset (\"water layer\") could be made opaque and light blue.\nWe thank the reviewer for this helpful suggestion. Changes made in Figure 4 as\nsuggested.\nReferences\nAretusini, S. et al. Fast and Localized Temperature Measurements During Simulated\nEarthquakes in Carbonate Rocks. Geophy. Res. Lett. 48,\ndoi:10.1029/2020gl091856 (2021).\nCornelio, C., Spagnuolo, E., Di Toro, G., Nielsen, S. & Violay, M. Mechanical\nbehaviour of fluid-lubricated faults. Nat. Commun. 10, 1274, doi:10.1038/s41467-\n019-09293-9 (2019).\nHan, R., Hirose, T., Shimamoto, T., Lee, Y. & Ando, J.-i. Granular nanoparticles\nlubricate faults during seismic slip. Geology 39, 599-602, doi:10.1130/g31842.1\n(2011).\nKitajima, H., Chester, J. S., Chester, F. M. & Shimamoto, T. High-speed friction of\ndisaggregated ultracataclasite in rotary shear: Characterization of frictional\nheating, mechanical behavior, and microstructure evolution. J. Geophys. Res.\nTogo, T. & Shimamoto, T. Energy partition for grain crushing in quartz gouge during\nsubseismic to seismic fault motion: An experimental study. J. Struct. Geol. 38,\n139-155, doi:https://doi.org/10.1016/j.jsg.2011.12.014 (2012).\nYao, L., Ma, S., Niemeijer, A. R., Shimamoto, T. & Platt, J. D. Is frictional heating\nneeded to cause dramatic weakening of nanoparticle gouge during seismic slip?\nInsights from friction experiments with variable thermal evolutions. Geophy. Res.\nLett. 43, 6852-6860, doi:https://doi.org/10.1002/2016GL069053 (2016).\nYao, L., Shimamoto, T., Ma, S., Han, R. & Mizoguchi, K. Rapid postseismic strength\nrecovery of Pingxi fault gouge from the Longmenshan fault system: Experiments\nand implications for the mechanisms of high-velocity weakening of faults. J.\nGeophys. Res. Solid Earth 118, 4547-4563, doi:https://doi.org/10.1002/jgrb.50308\n(2013).\nReviewer #2 (Remarks to the Author):\nThis paper presents new laboratory data on frictional behavior of simulated gabbro\nfaults over a broad range of slip velocities to meter-scale slip distances, systematically\ncontrasting the distinct responses associated with fluid in the forms of water in vapor,\nliquid and supercritical states. The data are of high quality, and they fill in a critical gap\nin our understanding of the coupling of phase transition of the saturating fluid and its\npotential subtle impacts on fault strength and stability. Plausible mechanisms related to\nwater-rock interaction and elastohydrodynamic lubrication are proposed herein to\ninterpret the experimental data. Both methodology and results are presented in details.\nWe would like to express our sincere gratitude to the reviewer for his/her positive\nassessment and the constructive comments. We have done our best to address his/her\ncomments as shown below.\nMy primary comments are on certain technical aspects and the Discussion.\nthe authors should specify what the width of the water-saturated slip zone was in their\nsimulations.\nThe width of the slipping zone in our model is 100 μm.\nIn light of the fact that, unfortunately, the gouge layer was not fully recovered after the\nexperiments, resulting in a thin recovered gouge layer. Based on previous experiments\nperformed, but at room temperature, in the presence of liquid water in solid gabbroic\nrocks (Violay et al., 2014,2015; Mizoguchi et al., 2006), we assigned a thickness of\n~100 μm to the slipping zone in our model. This information is now clarified in the\nMethods section (Line 433).\n“The slipping zone has a width of 100 μm.”\nL161 “However, further studies are required to quantify the role of chemical bonds of\nabsorbed water in fault slip zones” – exactly what types of studies do the authors\nenvision that can clarify this subtle process?\nIn our opinion, infrared spectroscopy, micro-Raman spectroscopy and hyper-Raman\nspectroscopy (Yu et al., 2020; Seki et al., 2020) could provide rich information on the\nmicrostructure and dynamics of hydrogen bonds of water. These may help us to better\nunderstand the role of absorbed water in affecting the frictional behavior of fault zones.\nWe have now added a few words to clarify this (Lines 182-184).\n“Further studies on the microstructure and dynamics of hydrogen bonds are required\nto quantify the role of absorbed water in affecting the frictional behavior of fault zones.”\nL171-174 “These estimated viscosities are in the range of those attained by a mixture\nor suspension of rock powders with water in liquid and supercritical states….” citing\nreferences 42 & 43” – the narrative here is misleading and seems to imply that there\nexist directly relevant measurements on these plausible values. The wording needs to\nbe cleaned up to explicitly provide the logical argument.\nThank you for the constructive comments. We rewrote these sentences as follows (lines\n9\n194-201).\n“Since the viscosity of the mixture increases significantly as the volume fraction of\npowder increases46,47, these estimated viscosities can be attained when the produced\nrock powders mix with water in either liquid (η = 9.0 x 10-5 Pa·s at T = 300 ℃, P\nH2O f\n= 10 MPa) or supercritical (η = 4.0 x 10-5 Pa·s at T = 400 ℃, P = 30 MPa) states.\nH2O f\nThis combination results in forming a “slurry-like” mixture or suspension, potentially\nfacilitating the activation of mixed lubrication.”\nL 304 L332-333 In which lab were these experiments conducted? Although they may\nhave been presented in earlier publications, relevant technical details on accuracy and\nprecision of measurements including slip distance, velocity, stresses, torque, pressure\nand temperature should also be provided here.\nThank you for pointing this out. We added the following text in the Methods section\n(Lines 365-366 and 396-404).\n“The experiments were performed in a Low to High-Velocity rotary shear machine,\nlocated at the State Key Laboratory of Earthquake Dynamics at Institute of Geology,\nChina Earthquake Administration (IGCEA)26, equipped with a dedicated hydrothermal\npressure vessel.”\n“Normal load was measured with a load cell with a resolution of 10 N. Shear torque\nwas recorded by the cantilever-type torque gauge consisting of a horizontal arm and a\npair of force gauges with a resolution of 0.01 Nm. Axial displacement (i.e., sample plus\nloading column) was measured by a linear variable differential transducer (LVDT) with\na resolution of 1 μm. The angular velocity and rotary angle were recorded with an\nencoder and a high-precision potentiometer, respectively. Pore pressure was measured\nby a pressure transducer (100 MPa full range with 0.01 MPa resolution) positioned\nbetween the outlet of the syringe pump and the inlet of the vessel. The temperature was\nmeasured by a K-type thermocouple (resolution 0.1℃) placed ~ 1 mm away from the\nslip surface.”\nL27 “faults”\nDone.\nL41 “is” -> are\nThanks, “is” has been replaced with “are”.\nL46 “for” -> For\nChange made.\nL78 “much extent”\nChange made.\nL163 “a-dimensional” -> “adimensional” or “nondimensional”\nChange made, thanks.\nReferences\nMizoguchi, K., Hirose, T., Shimamoto, T. & Fukuyama, E. Moisture-related weakening\nand strengthening of a fault activated at seismic slip rates. Geophys. Res. Lett. 33,\ndoi:10.1029/2006GL026980 (2006).\nYu, C.-C. et al. Vibrational couplings and energy transfer pathways of water’s bending\nmode. Nat. Commun. 11, 5977, doi:10.1038/s41467-020-19759-w (2020).\nSeki, T. et al. The bending mode of water: A powerful probe for hydrogen bond\nstructure of aqueous systems. J. Phys. Chem. Lett. 11, 8459-8469,\ndoi:10.1021/acs.jpclett.0c01259 (2020).\nViolay, M. et al. Effect of water on the frictional behavior of cohesive rocks during\nearthquakes. Geology 42, 27-30, doi:10.1130/g34916.1 (2014).\nViolay, M., Di Toro, G., Nielsen, S., Spagnuolo, E. & Burg, J. P. Thermo-mechanical\npressurization of experimental faults in cohesive rocks during seismic slip. Earth\n11\n\\Planet. Sc. Lett. 429, 1-10, doi:10.1016/j.epsl.2015.07.054 (2015).\nReviewer #3 (Remarks to the Author):\nThis manuscript presents results of experimental measurements of frictional properties\nof gabbro at high-temperature hydrothermal conditions. The authors used a confined\nrotary shear apparatus to investigate how friction evolves as a function of slip and slip\nrate, specifically focusing on the state of aqueous pore fluid. The authors conducted\nexperiments spanning 3 possible states of interstitial water: liquid, steam, and\nsupercritical fluid. This is important because transitions between the states may\nsignificantly affect the fluid properties, solid-fluid interactions, and frictional strength.\nSuch transitions can occur both as a function of depth, and as a function of slip rate\nwhen coseismic heating may substantially modify the local temperature on a slip\ninterface. The authors find that the fluid state indeed controls the frictional properties\nof gabbro: for liquid water, friction is both slip and velocity weakening, while for steam\n(vapor) and supercritical state, friction is nearly velocity-neutral (but still slip-\nweakening). The authors attribute such different behaviors in part to formation of clay\nminerals, which they verified using a post-experiment microscopy analysis. The\npresented results are new and warrant publication in Nature Communications. Overall,\nthe manuscript is well written and logically organized. The experimental procedures are\nwell documented, and the methods are state of the art. The results should be of interest\nto a broad readership, including, but not limited to, experimentalists, seismologists,\nmodelers, and field geologists. I recommend that this manuscript is published, pending\na moderate review to address several comments, as described below.\nWe would like to express our gratitude to the reviewer for acknowledging the\nimportance of our work. We also thank the reviewer for the constructive and insightful\ncomments that prompted us to carefully rethink the interpretations. We have done our\nbest efforts to respond to these comments as follows.\n12\n1) While the experimental part of the study is robust, I am less convinced by the\ninterpretation that appeals to the elasto-hydro-dynamic lubrication (EHDL) mechanism.\nFor this mechanism to work, the fluid has to be essentially incompressible. The latter\ncondition applies to water in a common liquid state, but not to water vapor or\nsupercritical fluid, both of which are highly compressible, and therefore would not be\nvery efficient at \"flattening\" the slip interface by elastic deformation. Between the three\nfluid stated, the EHDL would be most efficient in case of liquid water; however, the\nexperiments show that in this case the residual dynamic strength is nearly independent\nof the slip rate (Fig. 1a,b). Based on these arguments, the EHDL is an unlikely\nmechanism responsible for the observed variations in dynamic friction.\nThank you for raising this critical point. We agree with the reviewer that the\ncompressibility of water in vapor and supercritical states is significantly higher\ncompared to water in liquid state. However, we think that for the EHD to work the fluid\nflow must be incompressible, rather than the fluid being incompressible. In fluid\ndynamics, incompressible flow (isochoric flow) refers to a flow in which the material\ndensity is constant within a fluid parcel (Sambavaram and Sarin, 2001).\nThe fluid’s compressibility does not determine whether the fluid flow is classified as\nincompressible flow. However, it is worth noting that in the literature, the term\n“incompressible fluid flow” is sometimes simply called “incompressible fluid”\n(Brodsky et al., 2001). When the fluid compressibility is acceptably small, the flow is\nconsidered to be incompressible.\nThe EHD lubrication theory is fundamentally built on the fluid motion governed by the\nNavier-Stokes equation. The incompressible fluid flow is an important assumption in\nthe model derivation, with which the time derivative of the density can be neglected\nand the continuity equation reduces to (Brodsky et al., 2001):\n(cid:3083)(cid:3048) (cid:3083)(cid:3050)\n+ = 0 Eq.1\n(cid:3083)(cid:3051) (cid:3083)(cid:3053)\nIn our experiments, when the (equivalent) friction coefficient reaches steady-state\nvalues, the density of the fluid (or the density of the mixture of water and rock\n13\npowders) remains relatively constant. So it is reasonable to consider that, regardless of\nthe water state, the continuity equation can be validly written in the form of Eq 1.\nBased on these arguments, the EHD lubrication theory is still valid and can be\nconsidered a possible fault weakening mechanism. In fact, EHD lubrication theory\nprovides a quantitative relationship between the friction coefficient (μ) and the\nSommerfeld number (S), constraining three different regimes: boundary lubrication,\nmixed lubrication and hydrodynamic lubrication (Williams, 2005; Brodsky et al.,\n2001; Cornelio et al., 2019). In our study, we propose that the decrease in the friction\ncoefficient with slip distance occurs under the mixed lubrication regime (S ~ 0.001),\nwhere the normal stress is supported by both solid-solid contacts and the fluid.\nWe agree with the reviewer that the fluid with higher compressibility would enhance\nthe efficiency of “flattening” the slip interface. This would facilitate an elevation in\nnet pressure rise and result in a more pronounced EHD lubrication process.\nNonetheless, it is important to note that the mixture of rock powders and water rather\nthan solely pure water acts as the lubricant in our experiments. The compressibility of\nthe mixture may not exhibit significant variations in the cases of water in different\nphysical states. Moreover, the viscosity of the fluid is likely to be more important than\nits compressibility in order for the underlying lubrication mechanism to work. We\npropose that the mixture of produced gouges with liquid and supercritical water forms\na slurry-like lubricant to weaken the frictional strength, as summarized by Reviewer\n#1 “mixing of gouge particles with water produces a lubricant of appropriate\nviscosity to cause macroscopic weakening of the frictional interface”.\nBy taking into account the reviewers’ comments and our understanding of EHD, we\nchange the text as follows:\nLines 185: “Considering the presence of fluid between two rough surfaces,…”\nLine 208-211: “As a consequence, we propose that a viscous “slurry-like” mixture of\nrock powders and water can function as a lubricant, allowing a mixed EHD\nlubrication process that weakens the frictional interface. In fact, this process is\n14\nexpected to be more efficient in the case of liquid water, since its low compressibility\nenables the slurry to flatten elastically the micro-roughness of the sliding surface.”\nIn fact, figuring out the exact weakening mechanisms in these experiments is really\nchallenging, despite our intensive micro-analytical work conducted on the recovered\nsamples. We believe that these reproducible experimental data about the relation\nbetween the physical state of water and rock friction may require further studies to\ninvestigate the underlying weakening mechanisms.\n2) The authors do not mention thermal pressurization as a possible mechanism. Is this\nbecause the slip rates are too low to cause a large enough temperature increase? Please\nelaborate. (The argument about fluid compressibility raised above would also apply in\ncase of thermal pressurization.)\nWe thank the reviewer for reminding us to discuss the possible activation of thermal\npressurization (TP). As suggested by the reviewer, the temperature rises in most of our\nexperiments are negligible except for those performed at slip velocities of 10 mm/s\n(measurable) and 100 mm/s (significant; towards ~ 1000℃ within the slipping zone).\nHowever, TP involves competing processes between thermal and hydraulic diffusion\nwith several key parameters that are not well defined (e.g., slipping zone width,\npermeability and porosity, etc. especially how they may evolve during slip; see also\ndiscussion in Cornelio et al., 2022). In any case, we do not consider TP can be a possible\nweakening mechanism in our experiments for two main reasons:\n1. Cornelio et al., 2022 used an optimization procedure to match the mechanical data\nobtained by shearing solid rock in the presence of pressurized water with the predicted\nshear stress (that is, the dynamic frictional strength) due to the activation of thermal\npressurization. They showed that in high-velocity frictional experiments where the\nincrease of the temperature in the slipping zone is significant (about 1200℃), other\nweakening mechanisms are more suitable for explaining the mechanical data (see its\nSupplemental Figure 3, Cornelio et al., 2022).\n2. Given the imposed effective normal stress of 10 MPa, the maximum slip velocity V\n15\n= 100 mm/s is still not sufficiently high to cause TP capable of explaining the\nweakening observed in our experiments, as suggested by numerical modeling results of\nthermal pressurization shown below.\nWe built a finite element model with Comsol Multiphysics to estimate the pore pressure\nrise in the slipping zone (For a detailed model description, see Yao et al., 2023). The\nmodel’s geometry is built based on the real sample assembly used in the experiments.\nWe take temperature- and pressure-dependent properties of water into account. We\nassume the intrinsic friction coefficient as a constant value of 0.7. The modeling results\n(see Rebuttal Fig. 1) show that the observed weakening at V ≤ 10 mm/s cannot be\nexplained by TP as TP is negligible under these conditions. At V =100 mm/s, TP may\ncontribute somewhat to the observed weakening, but is still not the dominant weakening\nmechanism. In summary, TP process is unlikely to be a significant weakening\nmechanism in our experiments, especially in the cases of V ≤ 10 mm/s.\nWe have added the following text and Supplementary Figure 9 to emphasize this point\n(Lines 144-151).\n“The weakening measured at V= 100 mm/s could be attributed to several established\nweakening mechanisms (e.g., flash heating36,38, thermal pressurization31,39, frictional\nmelting40, etc.). We assess the weakening effect of thermal pressurization as an example\nvia numerical modeling39. The results show that only at V= 100 mm/s pore pressure\nincrease in the slipping zone could potentially contribute to the observed weakening\n(see supplementary Fig. 9). Flash heating is also likely to occur at V ≥ 100 mm/s in\naccordance to previous studies36,38. However, the weakening behavior observed at slip\nvelocities ≤ 10 mm/s cannot be explained by these mechanisms.”\n17\n3) All of the presented experiments exhibit evolution of friction from \"peak\" to \"steady\nstate\" over a characteristic distance of the order of 1 m (Fig.1 a,c,e). A similar evolution\n(although of smaller magnitude) was reported in rotary shear experiments on dry gabbro\n(e.g., www.nature.com/articles/nature11370). Could there be a common mechanism,\npossibly enhanced by the presence of fluid? Please discuss.\nThank the reviewer for bringing to our attention the results reported in Brown and\nFialko (2012), which is relevant to our work. The authors proposed that the formation\nof\nformation of hotspots and “melt welts” unload the rest of the slip surface in experiments\nperformed on gabbro. They observed dynamic fault weakening at slip velocities higher\nthan 0.06-0.2 m/s, primarily driven by the local formation of “melt welts”. We have\nnow cited this paper in the revised manuscript (ref. number 35). However, we do not\nbelieve that the weakening mechanism operating in their experiments is responsible for\nthe slip-weakening behavior observed in our experiments. The experiments described\nin Brown and Fialko (2012) were performed under room humidity conditions, and the\nlocal formation of frictional melts is the key to the weakening mechanism they proposed.\nEven if a similar mechanism were to operate in our experiments performed at the slip\nvelocity of 100 mm/s (comparable to 0.06-0.2 m/s), it cannot account for the weakening\nobserved at slip velocities of 1 to 4 orders of magnitude lower (10 μm/s to 10 mm/s).\nMore importantly, the complex fluid-rock interaction at elevated temperatures (300-\n400℃) and pore pressure (30 MPa), as in our experiments, differs significantly from\nthe conditions in the cases of Brown and Fialko (2012). As a consequence, we believe\nthat other mechanisms beyond the “melt welts” may operate in our experiments.\n4) line 35. Instead of \"at seismic deformation conditions\", consider \"at seismic slip\nrates\", or \"at seismogenic conditions\".\nDone, “seismic deformation conditions” has been replaced with “seismogenic\nconditions”.\n5) line 78. \"to a much extent\" -> \"to a much greater extent\".\nChange made as suggested.\n18\n6) line 90. \"After the experiments, the slip surfaces were ultra-polished and lineated\" -\nit would help to include a figure illustrating this, perhaps in Supplementary Materials.\nWe thank the reviewer for the suggestions. We have now added a figure (Supplementary\nFig. 4 in the revised manuscript) to illustrate the lineated slip surface. The term “ultra-\npolished” is supported by the RMS values of the slip surfaces (3.5-7.0 μm) derived\nfrom the roughness measurements (Fig. 2a-c).\nIn response to the reviewer’s comment, the following figure has been added as\nSupplementary Figure 4 in the revised manuscript.\nUpdated Supplementary Figure 4. “Close up” photographs of slip surfaces recovered from the\nexperiments performed at V= 10 μm/s. The slip surfaces are polished and striae are parallel to the\nslip vector. a. Experiment LHV2398, water in liquid state. b. Experiment LHV2380, water in\nsupercritical state. c. Experiment LHV2391, water in vapor state.\nReferences\nSreekanth R. Sambavaram, Vivek Sarin, (2002), Parallel Computational Fluid\nDynamics 2001.\nBrodsky, E. E. & Kanamori, H. Elastohydrodynamic lubrication of faults. J. Geophys.\nRes. Solid Earth 106, 16357-16374, doi:10.1029/2001jb000430 (2001).\nBrown, K. M. & Fialko, Y. 'Melt welt' mechanism of extreme weakening of gabbro at\nseismic slip rates. Nature 488, 638-641, doi:10.1038/nature11370 (2012).\nCornelio, C. et al. Determination of parameters characteristic of dynamic weakening\n19\nmechanisms during seismic faulting in cohesive rocks. J. Geophys. Res. Solid\nEarth 127, e2022JB024356, doi:https://doi.org/10.1029/2022JB024356 (2022).\nWilliams J., 2005. Engineering Tribology. Cambridge University Press.\nYao, L., Ma, S. & Di Toro, G. Coseismic fault sealing and fluid pressurization during\nearthquakes. Nature Communications 14, 1136, doi:10.1038/s41467-023-36839-9\n(2023).\n20"}, {"round": 2, "reviewer_comments": {"reviewer_1": "Dear Editor,\nRegarding the revised manuscript titled \"Physical state of water controls friction of gabbro-built\nfaults\" by Feng et al., I would like to let you know that, in my opinion, the authors have addressed\nall of the points I raised in my review in a satisfactory manner. Furthermore, I believe that the\nauthors have presented reasonable arguments in addressing the issues raised by the other\nreviewers.\nI remain at your disposal for any further questions.\nYours faithfully,\nReviewer #1", "reviewer_2": "In revising the manuscript, the authors have basically address my concerns raised in my earlier\nreview in an adequate manner.", "reviewer_3": "The authors have done a good job with their revision. I agree that the viscosity of a fluid/gouge\naggregate likely plays a more important role than its compressibility, however I am not convinced\nthat compressibility of a \"slurry\" is controlled by compressibility of solid (i.e., gouge)\nparticles. When the effective normal stress is primarily supported by a solid phase (which would be the case\nfor a highly compressible fluid), the shear zone material is no longer a slurry. Also, because of the\nrelatively short wavelengths of the \"bumps\" on a sample interface, the elastic flattening\nwould require very high overpressure. The bottom line is that the hydrodynamic lubrication may well be\ninvolved, while the elastohydrodynamic lubrication is less likely.\nI also agree with the authors that melting is unlikely involved in their experiments, at\nleast at the macroscopic level. My comment was referring to the \"early evolution\"\nstage of the dry gabbro experiments (Fig. 1 in Brown & Fialko, 2012) which looks similar to\nthe results presented by the authors. If the authors have conducted any experiments at\ndry conditions, it would be instructive to include (or at least describe) the respective\nresults. I understand that their apparatus might not permit experiments at dry conditions.\nThe above comments are secondary to the main contributions of this manuscript, and I leave it to\nthe authors whether to consider them any further. I congratulate the authors on a nice\ncontribution."}, "author_response": "Response to reviewers’ comments\nWe would like to express our gratitude to all three reviewers for their time and\nconstructive comments on our revised manuscript titled “Physical state of water\ncontrols friction of gabbro-built faults”. Below, you will find our point-by-point\nresponse (blue fonts) to the reviewers’ comments (black fonts).\nReviewer #1 (Remarks to the Author):\nDear Editor,\nRegarding the revised manuscript titled \"Physical state of water controls friction of\ngabbro-built faults\" by Feng et al., I would like to let you know that, in my opinion, the\nauthors have addressed all of the points I raised in my review in a satisfactory manner.\nFurthermore, I believe that the authors have presented reasonable arguments in\naddressing the issues raised by the other reviewers.\nI remain at your disposal for any further questions.\nYours faithfully,\nReviewer #1\nWe thank Reviewer #1 for the positive assessments.\nReviewer #2 (Remarks to the Author):\nIn revising the manuscript, the authors have basically address my concerns raised in my\nearlier review in an adequate manner.\nWe thank Reviewer #2 for the positive assessments.\nReviewer #3 (Remarks to the Author):\nfluid/gouge aggregate likely plays a more important role than its compressibility,\nhowever I am not convinced that compressibility of a \"slurry\" is controlled by\ncompressibility of solid (i.e., gouge) particles. When the effective normal stress is\nprimarily supported by a solid phase (which would be the case for a highly compressible\nfluid), the shear zone material is no longer a slurry. Also, because of the relatively short\nwavelengths of the \"bumps\" on a sample interface, the elastic flattening would require\nvery high overpressure. The bottom line is that the hydrodynamic lubrication may well\nbe involved, while the elastohydrodynamic lubrication is less likely.\nWe agree with the reviewer that the compressibility of a slurry-like mixture of powders\nand water may not be mainly controlled by the solid phase. Therefore, if the fluid is\ncompressible (e.g., supercritical water) the normal stress will be supported by the solid\nphase. In this case, the elastic effect of fluid in flattening the slip surface may be limited.\nInstead, the hydrodynamic lubrication may operate through the lubricated solid-solid\ncontacts by the slurry-like film. To clarify this point according to the comments from\nthe reviewer, we added additional discussion on Lines 201-203.\n“Such elastic flattening effects may not operate in the case of supercritical water that\nis more compressible, hydrodynamic lubrication can be activated through the presence\nof a slurry-like film in solid-solid contacts.”\nI also agree with the authors that melting is unlikely involved in their experiments, at\nleast at the macroscopic level. My comment was referring to the \"early evolution\"\nstage of the dry gabbro experiments (Fig. 1 in Brown & Fialko, 2012) which looks similar to\nthe results presented by the authors. If the authors have conducted any experiments at\ndry conditions, it would be instructive to include (or at least describe) the respective\nresults. I understand that their apparatus might not permit experiments at dry conditions.\nWe thank the reviewer for clarifying further the comment in the 1st round review. We\nstill believe that the results reported by Brown and Fialko, 2012 are not directly\n2\ncomparable to the results shown in Figure 1 in the main text. As the reviewer\nacknowledged, the “melt welts” mechanism proposed in their paper is unlikely\nactivated in our experiments. Since the reviewer is curious about the experimental\nresults at dry conditions, we show the evolution of friction coefficient with slip for the\nonly experiment we performed at room temperature and dry conditions in Rebuttal\nFigure 1. In fact, this experiment is designed for other research purposes, the\nexperiment was stopped several times during slip. Nonetheless, it is clearly shown that\nno weakening in friction coefficient occurred within the initial 100 mm of slip distance\nat dry conditions we investigated. We apologize for not being able to provide more\nintuitive data at this moment.\nIn the main text, we simply added “under room humidity” on Line 138 and cited this\nrelevant paper (ref. 35).\nRebuttal Figure 1 Experiment LHV2450 performed at room temperature (~25℃), pore\npressure of 0 MPa (dry) and 10 MPa effective normal stress, at a slip velocity of 100\nμm/s.\nleave it to the authors whether to consider them any further. I congratulate the authors\non a nice contribution.\nThanks to Reviewer #3 for acknowledging the contributions of our work.\n4"}]

Decision letter