Constitutive Behavior of Olivine Gouge Across the Brittle‐Ductile Transition

The bottom of the lithosphere is characterized by a thermally controlled transition from brittle to ductile deformation. While the mechanical behavior of rocks firmly within the brittle and ductile regimes is relatively well understood, how the transition operates remains elusive. Here, we study the mechanical properties of pure olivine gouge from 100 to 500°C under 100 MPa pore‐fluid pressure in a triaxial deformation apparatus as a proxy for the mechanical properties of the upper mantle across the brittle‐ductile transition. We describe the mechanical data with a rate‐, state‐, and temperature‐dependent constitutive law with multiple thermally activated deformation mechanisms. The stress power exponents decrease from 70 ± 10 in the brittle regime to 17 ± 3 and 4 ± 2 in the semi‐brittle and ductile regimes, respectively. The mechanical model consistently explains the mechanical behavior of olivine gouge across the brittle‐ductile transition, capturing the gradual evolution from cataclasis to crystal plasticity.

• The mechanical properties of olivine gouge provide a proxy for the brittle-to-ductile transition in the upper mantle • Olivine gouge follows rate-and state-dependent friction at low temperatures and high strain rates and rate-dependent plasticity otherwise • The brittle-ductile boundary includes a semi-brittle regime operating within a temperature range of 100°S upporting Information: Supporting Information may be found in the online version of this article. 10.1029/2023GL105916 2 of 11 the ductile layers, deformation is distributed and controlled by thermally activated creep mechanisms (Bürgmann & Dresen, 2008;Evans & Kohlstedt, 1995;Masuti et al., 2016).Across the brittle-ductile transition, the constitutive law turns from a rate-and state-dependent behavior to a rate-dependent flow law with a high stress power exponent of n = 17 in halite at room temperature with increasing independence to effective normal stress (Shimamoto, 1986).At temperatures ranging from 185 to 500°C, in the semi-brittle regime, halite follows a power-law flow law with a stress exponent of 13 ± 8 for the direct effect, reducing to about 8.5 at steady state, associated with an activation enthalpy of about 125 kJ/mol (Noda & Shimamoto, 2010).Deformation experiments on granitoid gouge yield stress exponents as high as 140 in the brittle regime, decreasing gradually to 10 in the semi-brittle domain, associated with increasing activation energies from 80 to 180 kJ/mol (Pec et al., 2016).Such transition to plasticity at low strain rates or high temperatures is also observed in synthetic and natural gouge with composite mineral compositions (Bos & Spiers, 2002;Blanpied et al., 1995;den Hartog et al., 2012aden Hartog et al., , 2012b;;Niemeijer et al., 2016;Okuda et al., 2023;Verberne et al., 2015).
The clearest evidence for a gradual transition from frictional slip to plasticity in the semi-brittle regime comes from joint analyses of mechanical data and microstructure.Phyllosilicate-rich mylonites exhibit Riedel shear zones surrounded by a fine-grain matrix in the brittle regime, but more pervasive deformation with S-C mylonitic microstructure in the semi-brittle field (Zhang & He, 2016).Laboratory experiments on calcite gouge at 550°C show a flow-to-friction transition within increasing slip rates characterized by well-compacted, homogeneous texture and crystallographic preferred orientation at low slip-rate, and localized shear bands at high strain-rates (Chen et al., 2020).In the semi-brittle regime, the stress power exponent falls in the range of 2.5-8.8,suggesting a mixture of dislocation and diffusion creep (Chen et al., 2020).Overall, the brittle-ductile transition is controlled by the complex interplay of temperature, slip-rate, and normal stress (Blanpied et al., 1995;Chen et al., 2020;Shimamoto, 1986;Zhang & He, 2016).The laboratory observations discussed above combined with field evidence for seismic unrest in the semi-brittle domain (Jamtveit et al., 2018;Petley-Ragan et al., 2019) put into question the constitutive behavior and seismogenic potential of rocks at the brittle-ductile transition.However, previous laboratory work on the strength of the oceanic lithosphere does not traverse the brittle-ductile transition within experimental conditions (Boettcher et al., 2007;King & Marone, 2012).
Here, we study the mechanical properties of pure olivine gouge as a function of temperature in wet conditions as a proxy for the brittle-ductile transition in the upper mantle.We conduct velocity-step experiments in a triaxial apparatus with an effective normal stress of 150 MPa under a pore fluid pressure of 100 MPa.We document the frictional strength from 100 to 500°C and explain the mechanical data with a physical model that captures the brittle, semi-brittle, and ductile behaviors consistently.In Section 2, we present the methodology and laboratory results.In Section 3, we describe the constitutive model and calibrate the thermodynamic parameters to explain the mechanical behavior in the brittle, semi-brittle, and ductile regimes.These findings provide a consistent representation of the strength of the lithosphere as a function of strain rate and temperature.

Experimental Constraints
We use Damaping olivine from a pyroxenite peridotite xenolith ore deposit at Damaping, Zhangjiakou city, Hebei Province, China (Jin et al., 1994).The outcrop is situated at 114.543311°E, 40.972262°N.Analysis of scanning electron microscopy with energy dispersive spectroscopy indicates a magnesium-rich olivine, that is, forsterite.We conduct velocity-step experiments on a triaxial shear machine.The olivine block sample is first crushed and sieved through a 200-mesh to obtain a powdered gouge with a grain size <74 μm.A 1-mm-thick gouge layer is then sandwiched between two forcing blocks made of gabbro with a saw-cut inclined at 35°.The saw-cut surfaces are roughened with 200# abrasive and a hole on the upper forcing block provides direct access of the pore fluid to the gouge layer.The sample assembly is described in detail by Zhang et al. (2017) and a diagram of the apparatus is shown in Figure S1 in Supporting Information S1.
The experiments are conducted with a pore fluid pressure of 100 MPa and a macroscopic normal stress of 250 MPa, resulting in an effective normal stress of 150 MPa.To determine the velocity dependence of the effective friction coefficient, defined as the ratio of shear to effective normal stress, we switch the axial loading rates in a sequence initiated at 1.0 µm/s, with down-steps to 0.2 and 0.04 μm/s followed next by up-steps to 0.2 and 1 μm/s.We start the sequence shortly after yielding occurs within the sample.The sequences at each imposed velocity occupy approximately the same slip distance.We conduct the sequence twice over a cumulative load point displacement of less than 4 mm.Due to the oblique geometry of the saw cut, the local slip rate along the 10.1029/2023GL105916 3 of 11 interface is 22% higher than the loading rate at the piston.We repeat the experiments using different samples from the same lithology at temperatures between 100 and 500°C by steps of 100°C.We then conduct post-mortem scanning electron microscopy on the deformed samples.
The mechanical response to velocity steps depends on the ambient temperature and slip rate (Figure 1).In the first velocity-step sequence, we always observe spurious oscillations or stick-slip events, compatible with velocity-weakening behavior at all temperatures, as previously observed (Boettcher et al., 2007).The behavior is more stable in the second sequence, which we attribute to textural maturation with cumulative slip.We, therefore, focus the analysis on the second velocity-step sequence.At 100°C and 200°C, the frictional behavior is rate-and state-dependent.The direct effect manifests itself gradually due to the sample and machine stiffness and is followed by an evolutionary phase to a new steady-state frictional level.The velocity steps impose a change of the friction coefficient by only a few percent from the initial level.At 100°C, the frictional response is velocity strengthening at all imposed velocities.At 200°C, the system appears weakly velocity weakening, as evidenced by the telltale opposite direct and steady-state responses.A transition to rate-dependent creep occurs at 300°C.For the first velocity step of the second sequence from 1.22 to 0.244 μm/s, the velocity-strengthening response does not differ markedly from the behavior at 100°C.However, with decreasing slip rates and increasing cumulative slip, the amplitude of the response increases drastically and the evolution of the friction coefficient becomes monotonic, without clear evidence for a state evolution.The amplitude of the rate-dependent response increases further at higher temperatures.At 400°C, a velocity step from 0.244 to 0.048 μm/s induces a change of friction from 0.58 to 0.5, a difference of 16%.At 500°C, changing the slip rate from 1.22 to eventually 0.048 μm/s reduces the apparent friction coefficient from 0.65 to 0.51, representing a 27% change.
To characterize the mechanical properties quantitatively, we describe the frictional response within the empirical framework of rate-and state-dependent friction (Dieterich, 1979;Rice & Ruina, 1983;Ruina, 1983).Key characteristics are the velocity dependence for the direct effect, defined as and the velocity dependence at steady-state, defined as We analyze the mechanical data using the RSFit3000 methodology (Skarbek & Savage, 2019) providing best-fit parameters using the aging law (Table S1 in Supporting Information S1) and the slip law (Table S2 in Supporting Information S1) proposed by Ruina (1983).In the 100-200°C range, the data can be reasonably well explained by the empirical model, yielding a = 0.0058 ± 0.0016 with a − b = 0.0021 ± 0.0004 and a − b = −0.0025± 0.001 in the velocity-strengthening (100°C) and velocity-weakening (200°C) regimes, respectively.The empirical model is less well suited to explain the mechanical data in the rate-dependent creep regime at and above 300°C, requiring either unphysical parameters to fit the data well or providing a less satisfactory fit for reasonable parameters (e.g., based on sub-metric characteristic weakening distance), as previously reported (Chen et al., 2020;King & Marone, 2012).To gain more insights into the underlying process, we estimate the direct-effect parameter a by grid search assuming b = 0. We find a = 0.019 ± 0.014, a = 0.037 ± 0.012, and a = 0.042 ± 0.008 for the temperatures of 300, 400, and 500°C, respectively.These results indicate a drastic increase of the direct effect parameter across the friction-to-flow transition and a further gradual increase with temperature within the rate-dependent creep regime.
The experimental data reveal a complex mechanical response characterized by three distinct regimes of stability and constitutive behavior.At low-temperature, high slip-rate conditions, wet Damaping olivine exhibits a frictional behavior with a slip-rate and state dependence that can be adequately captured by empirical friction laws.
The frictional regime can be subdivided into temperature ranges of velocity-strengthening and velocity-weakening at steady state, with the stability transition occurring between 100 and 200°C.At high-temperature, low slip-rate conditions, the mechanical response transitions to rate-dependent creep with a drastic increase of the rate dependence leading to a marked reduction of the apparent friction coefficient at low slip rates.
Scanning electron microscopy of the deformed samples reveals a distinct microstructure for the frictional and creep regimes (Figures 1b and 1c, Figure S2 in Supporting Information S1).At 100°C and 200°C, the deformation is highly localized along comminuted Riedel shear zones.The dominant feature is R 1 shear zones that traverse the gouge from wall to wall.Less developed Y-shear and P-shear can be found near the boundary.There is no distinct microstructure for the velocity-strengthening (100°C) and velocity-strengthening (200°C) samples.However, deformation is more distributed for the 300, 400, and 500°C samples, with more comminution by boundary shear near the blocks.The more frequent presence of large clasts indicates the diminished role of fracturing in this temperature range.There is no distinct microstructure for the semi-brittle and ductile regimes, compatible with previous findings for San Carlos olivine (King & Marone, 2012).

Mechanical Model
We describe a physical model that captures the three distinct mechanical regimes of Damaping olivine characterized by rate-and state-dependent friction at low temperatures with a velocity-strengthening to velocity-weakening transition between 100 and 200°C followed with increasing temperature by a friction-to-flow transition at about 300°C with increasing dependence on slip rate.This complex behavior can be described by the following constitutive law that combines frictional sliding and two thermally activated creep mechanisms related to semi-brittle and ductile flow (Barbot, 2023) 10.1029/2023GL105916 5 of 11 )] , (3) where V and V 0 are the instantaneous and reference slip rate, d and d 0 are the size of micro-asperities at contact junctions and a characteristic size, τ and τ 0 are the shear stress and a reference value, and T is the absolute temperature (Barbot, 2019a).The instantaneous velocity of sliding results from the potential contribution of three thermally-activated mechanisms with the activation energies Q 1 , Q 2 , and Q 3 and the temperatures of activation  T1 ,  T2 , and  T3 assuming an Arrhenius temperature dependence.The universal gas constant R represents a thermal energy per unit mole per unit degree of temperature.The first mechanism is rate-and state-dependent with the frictional strength defined by the apparent cohesion c 0 , the reference coefficient of friction μ 0 , and the effective normal stress    = 150 MPa that includes the Terzaghi effect of pore fluid pressure.Rapid sliding occurs when the shear stress approaches or exceeds the yield strength due to a power exponent n 1 ≫ 1.The frictional strength is modulated by the size of micro-asperities and the ambient temperature.The negative power-law exponent −m 1 corresponds to an increase in frictional strength with asperity size.The subsequent terms describe two rate-dependent creep mechanisms for semi-brittle and ductile deformation, respectively, organized with decreasing stress power exponents and increasing energies and temperatures of activation.We introduce the reference stress τ 0 such that all the terms in parenthesis are unitless.However, the constants τ 0 and  T2 are not independent and trade-off with each other.One cannot constrain τ 0 and  T2 individually.The same trade-off applies for τ 0 and  T3 for the third term.
The presence of multiple healing mechanisms is attributed to subcritical crack growth with possible stress corrosion and pressure-solution creep around micro-asperities enabled by high pore-fluid pressure.The competition between healing mechanisms can be captured in the constitutive framework with the aging-law end-member evolution law in isobaric conditions (Barbot, 2022) allowing healing at stationary contact, where G 1 and G 2 are reference rates of contact healing, p 1 and p 2 are grainsize sensitivity exponents, and the Arrhenius activation is controlled by the activation energies H 1 and H 2 and the activation temperatures T 1 and T 2 .Healing is counter-balanced by contact rejuvenation with shear strain within the gouge, which is controlled by the gouge thickness h and a reference strain-rate 1/λ, affecting the temperatureand velocity-dependent steady-state strength.Another formulation for the competition of healing mechanisms that falls within the slip-law end-member (Barbot, 2022) is shown in Equation S2 in Supporting Information S1.
We calibrate the constitutive parameters of wet Damaping olivine gouge based on the mechanical data in Figure 1.We simulate velocity steps numerically using a spring-slider assembly with finite stiffness, where the slider obeys the constitutive laws of Equations 3 and 4. For each velocity step, we assume that the mechanical system is at steady-state at velocity V 1 followed by a sudden change of loading rate to a velocity V 2 , taking the values of 1.22, 0.244, and 0.0488 μm/s.The constitutive equations do not afford closed-form solutions for the steady state, so we resolve to numerical solutions.We calculate the evolution of the frictional strength  ∕ σ using a fifth-order accurate Runge-Kutta method (Press et al., 1992).To determine the best-fitting constitutive parameters, we use a grid search (Figure S3 in Supporting Information S1).We determine the uncertainties of the parameters using the range of values within 10% of the lowest residuals.
Most observations can be reproduced using constant constitutive parameters (Figure 2).The rate-and state-dependent regime can be explained with the reference friction coefficient μ 0 = 0.58 and the reference velocity V 0 = 1 μm/s.The thermally activated power-law is characterized by a stress power exponent n 1 = 70 ± 10, the activation energy Q 1 = 40 ± 10 kJ/mol associated with the activation temperature  T1 = 20 • C. The transition from steady-state velocity-strengthening at 100°C to velocity-weakening at 200°C can be explained by the competition between two healing mechanisms with activation energy H 1 = 10 kJ/mol and H 2 = 70 kJ/mol, activation temperature T 1 = 0°C and T 2 = 180°C, with power-law exponents p 1 = 2.2 m 1 and p 2 = 0.9 m 1 with a asperity-size exponent m 1 = 3.5.The thermodynamic parameters for healing are commensurate with those of other pure and synthetic gouge (Barbot, 2022(Barbot, , 2023)).The friction-to-flow transition is captured by the activation of the rate-dependent creep mechanisms.The semi-brittle regime that activates at 300°C is characterized by a thermally activated power-law relationship with a stress power exponent n 2 = 17 ± 3, an activation energy Q 2 = 240 ± 50 kJ/mol and an activation temperature  T2 = 318 • C. Finally, the ductile regime is defined by another power-law relationship with n 3 = 4 ± 2 and Arrhenius activation parameters Q 3 = 300 ± 100 kJ/mol and  T3 = 430 • C. All the parameters are shown in Table S3 in Supporting Information S1.S3 in Supporting Information S1.
The velocity-step data and the model predictions are shown in Figure 2. In the low-temperature velocity-strengthening regime, the model captures the direct effect smoothed by finite stiffness and the evolution to a high-resistance steady-state level after a slip distance of about 50 μm.At 200°C, the model captures the near-neutral weakening with a weak oscillation for the 0.244-to-0.0488μm/s down-step.The model slightly over-predicts the direct effect of the final up-step.The experiments at 300°C mark the friction-to-flow transition.The model predicts velocity-strengthening friction for the first down-step to 0.244 μm/s and the transition to rate-dependent creep at 0.0488 μm/s with a much higher rate-dependence.At 400°C, the model reproduces well the velocity steps of the first sequence, although with some residuals for the final up-step.Finally, the model captures the increased sliprate dependence of creep at 500°C.In this regime, the physical model explains the mechanical data better than the empirical friction law, presumably because the power-law formulation is better suited than an exponential form.
The last up-step to 0.244 μm/s is poorly explained, but steady-state was not reached after the previous velocity step, raising doubts about the significance of these final observations.The constitutive parameters are the same in all conditions, explaining the slight misfit observed for various cases.Using the slip-law end-member of the evolution law (Barbot, 2022) provides an equally satisfactory fit to the mechanical data (Figure S4 in Supporting Information S1).
Once calibrated to observations, the physical model can be used to extrapolate the mechanical behavior of olivine outside the laboratory conditions, particularly at lower and higher slip rates.To delineate the stability regimes and the brittle to semi-brittle and semi-brittle to ductile transitions, we evaluate the empirical parameters a and a − b defined in Equations 1 and 2, respectively, predicted by the model.We conduct numerical velocity steps at infinite stiffness to determine the slip-rate dependence of shear stress for the direct effect and at steady-state at different temperatures (Barbot, 2022).The comparison between model predictions and observations is shown in Figure 3.
The distribution of the steady-state parameter a − b delineates three regimes of stability with a central rate-weakening domain with temperature bounds depending on slip rate.At nanometers per second, which is representative of slip-rates for creep and earthquake nucleation, the seismogenic zone extends from 100 to 200°C, but at high slip rates, for example, 100 μm/s, the steady-state velocity-weakening region stretches from 230 to 320°C.Within the entire frictional domain, from room temperature to about 250°C on average, the direct effect parameter is constant, in agreement with laboratory observations.In the brittle field, the transition from velocity-strengthening at low temperatures to velocity-weakening at high temperatures is caused by the thermal activation of the second healing mechanism, leading to a different evolutionary response.Specifically, the change of a − b is caused by a change in b at constant a.
The third regime is characterized by a friction-to-flow transition at a temperature threshold depending on slip-rate.The transition occurs at 230°C at nanometers per second, but at 350°C for a slip rate of 100 μm/s.The brittle-to-ductile transition involves a separate stage of semi-brittle deformation characterized by a gradual increase of the direct effect parameters by about a factor of two.The transition to ductile deformation occurs at temperatures above 400-500°C, depending on slip rate, with a direct effect parameter about 10 times higher than in the frictional regime.

Discussion
The mechanical data for wet Damaping olivine gouge indicates a gradual transition from frictional sliding to rate-dependent creep with increasing temperature or decreasing slip rate.The change of deformation mechanism is characterized in the microstructure by a transition from localized deformation within comminuted shear zones in the frictional regime to more distributed deformation in the creep regime.However, as all samples experienced some degree of stick-slip during the first up-and-down step sequence, the post-mortem samples do not solely reflect the creep behavior at low slip-rate and high-temperature conditions.
A physics-based constitutive framework can explain these observations, unifying previous friction and flow laws that operate strictly in the brittle and ductile regimes, respectively.The brittle-to-ductile transition involves an intermediate step characterized by semi-brittle deformation for a finite range of temperature of about a hundred degrees with the lower and upper bounds depending on the instantaneous slip-rate.The frictional regime can be explained by a rate-, state-, and temperature-dependent friction law with a power-exponent of 70 ± 10 and an activation energy of 40 ± 10 kJ/mol, compatible with other synthetic and natural gouges (Barbot, 2019a(Barbot, , 2022(Barbot, , 2023)). 10.1029/2023GL105916 8 of 11 The semi-brittle regime is characterized by a power exponent of 17 ± 3 and an activation energy of 240 ± 50 kJ/ mol, sitting halfway between typical values for friction and the low power exponents of crystal plasticity.The ductile regime is reached at temperatures of about 400-500°C with a power-law exponent of 4 ± 2 and activation energy of 300 ± 100 kJ/mol.Although the microstructure does not identify these mechanisms, the lower stress power exponent suggests the activation of dislocation creep, grain boundary sliding, or pressure solution creep of wet olivine, albeit with a small activation energy (Hirth & Kohlstedt, 2003;Karato & Jung, 2003;Mei & Kohlstedt, 2000b).
Our findings on wet Damaping olivine are consistent with previous work on dry San Carlos olivine (King & Marone, 2012).In dry conditions, the brittle to semi-brittle transition occurs at higher temperatures between 800 and 1,000°C.The constitutive model presented in Section 4 reproduces the dry San Carlos olivine velocity-step data, including the evolution of the direct and steady-state velocity parameters and the characteristic weakening distance with slip-rate and temperature (Figures S5 and S6 in Supporting Information S1) and the detailed mechanical response upon up-steps (Figure S7 in Supporting Information S1), all at constant constitutive parameters (Table S4 in Supporting Information S1).In these dry conditions, the transition to ductile flow occurs at much higher temperatures.The energies and temperature of activation of the healing and deformation mechanisms are greater, compatible with the dependence of thermodynamic parameters on water fugacity (Mei andKohlstedt, 2000a, 2000b;Karato & Jung, 2003).Accordingly, the semi-brittle to brittle transition is not encountered below 1,000°C.S1 in Supporting Information S1. 10.1029/2023GL105916 9 of 11 Our results on wet Damaping olivine allow us to better predict the mechanics of the brittle-ductile transition in the upper mantle.In the oceanic lithosphere, the brittle-ductile transition depth is a sensitive function of plate age.We use a half-space cooling model to build a temperature profile for a 60 Myr-old oceanic plate assuming a mantle temperature of 1,400°C and typical heat capacity, mass density, and thermal conductivity for the oceanic mantle (e.g., Stein & Stein, 1992).We discuss the strength of the oceanic lithosphere for strike-slip faulting assuming near-lithostatic pore-fluid pressure resulting in a maximum effective normal stress of 150 MPa.To keep the discussion general, we focus on the temperature dependence (as opposed to depth dependence) of lithospheric strength based on olivine rheology (Figure 4).The strength profiles is a sensitive function of slip rate across the shear zone, with the friction-to-flow transition occurring at 250, 350, and 450°C at slip-rates of 1 nm/s, 1 μm/s, and 1 mm/s, respectively.The semi-brittle regime intervening between the friction and ductile domains operates within a 100-degree temperature range, relatively insensitive to slip rate.The temperature of the brittle and semi-brittle regimes at high slip-rate coincides with the distribution of oceanic intraslab earthquakes (Stein et al., 1992), with seismogenic behavior up to 700°C.Hence, the propagation of earthquakes in the oceanic upper mantle may involve thermal weakening in the semi-brittle and ductile regimes due to dynamic shear heating, as presumably occurred during the 2012 Mw 8.6 Indian Ocean earthquake (Wei et al., 2013).

Conclusions
The brittle-to-ductile transition is a dynamic property of the lithosphere, instead of a static property dictated by the frictional strength predicted by rate-independent Coulomb friction (Byerlee, 1978;Coulomb, 1821)  and the shear stress of crystal plasticity at constant strain-rate (Bürgmann & Dresen, 2008).A wide dynamic range of slip rates can be attained during seismic cycles, following seismic ruptures, afterslip, and creep waves (Barbot, 2019b;Tse & Rice, 1986;Wang & Barbot, 2023).Accordingly, the seismic cycle modulates the depth of the brittle-ductile transition (Barbot, 2018).Reciprocally, the bottom of the seismogenic zone corresponds to the transition from the brittle to the semi-brittle regime, characterized by a change from rate-and state-dependent friction to purely rate-dependent creep.Our laboratory observations and physical interpretation clarify the nature of the brittle-ductile transition in the upper mantle, providing important new constraints for the development of realistic models of seismic cycles within the lithosphere-asthenosphere system.

Figure 1 .
Figure 1.Frictional resistance of Damaping olivine to sliding at imposed velocity and microstructure.(a) Velocity-step experiments.In a first sequence, we impose velocity down-steps starting at 1.22 μm/s to 0.244 and 0.0488 μm/s followed by up-steps to 0.244 and 1.22 μm/s.Except for the experiment at 400°C, we repeat the sequence of velocity steps a second time.The experiments are conducted at 100°C (dark blue), 200°C (light blue), 300°C (purple), 400°C (yellow), and 500°C (orange).We always observe spurious oscillations or stick-slip events in the first sequence but the results are more stable in the second sequence.The mechanical response to velocity steps is rate-and state-dependent in the 100-200°C range, transitioning to purely rate-dependent at and above 300°C.At 300°C, the transition depends on slip-rate.Steady-state velocity-weakening can be observed at 200°C.(b) Representative microstructure from scanning electron microscopy for the deformed sample at 100°C showing intense shear around Riedel shear zones.(c) Microstructure for the sample deformed at 400°C showing more distributed deformation.More details are shown in Figure S2 in Supporting Information S1.

Figure 2 .
Figure 2. Observations (color by temperature) and physical model (black) of the transition from cataclastic flow to rate-dependent creep in olivine gouge from 100 to 500°C.The velocity step for each column is indicated at the top.The change of friction is relative to the value at the onset of the velocity step.The residuals between model and observations are shown in gray, shifted by 0.025 for better visibility.The slip-rate and state dependence of friction is apparent in the velocity-strengthening regime at 100°C and the velocity-weakening regime at 200°C.Data and model show a transition to rate-dependent creep at 300°C for slip-rate ≤0.244 μm/s and at higher temperatures for any slip-rate.The model is based on the constant constitutive parameters listed in TableS3in Supporting Information S1.

Figure 3 .
Figure 3. Mechanical properties of olivine gouge based on laboratory measurements with the empirical friction law (colored up triangles for up-steps and down triangles for down-steps) and prediction of the physical model (background color) for (a) the steady-state velocity dependence parameter a − b and (b) the direct effect parameter a, as a function of temperature and slip-rate.The empirical frictional parameters are listed in TableS1in Supporting Information S1.

Figure 4 .
Figure 4. Prediction of the strength of olivine across the brittle, semi-brittle, and ductile fields as a function of temperature and slip-rate.We assume a constant effective normal stress above 50°C.The variation of strength in the brittle field features regions of temperature hardening and temperature softening.The depth and width of the seismogenic zone depend on temperature and slip-rate.The transition to ductile deformation involves a finite range of temperature with semi-brittle deformation characterized by a distinct thermal activation of strength.The temperature at which semi-brittle deformation begins, marking the beginning of the brittle-ductile transition, varies from 250°C to 450°C depending on slip-rate.The frequency of oceanic intraslab earthquakes (black line)(Stein & Stein, 1992)  coincides with the brittle and semi-brittle regimes at high slip-rates.