Transition From Slow to Fast Injection-Induced Slip of an Experimental Fault in Granite Promoted by Elevated Temperature

The influence of elevated temperature on injection-induced fault slip is poorly constrained. In this study, at steady-state elevated temperatures, triaxial shear-flow experiments on a sawcut fault in granite were conducted to simulate injection-induced slip of a critically stressed fault. Our results suggest that an elevated temperature favors a more uniform fluid pressure distribution over the fault surface mainly by reducing water viscosity. At temperatures above ambient, a larger perturbation force from the injected fluid is required to reactivate the fault primarily because of the enhanced thermally activated fault healing processes, resulting in a faster fault slip rate upon failure. This study may partially explain the causal link between higher reservoir temperature

In geothermal systems, the temperature contrast between the reservoir rock and the colder injected fluid near the injection well may cause the contraction of the reservoir and unclamp the fault.Both laboratory (KC & Ghazanfari, 2021) and numerical (Huang et al., 2019) studies demonstrate that the cooling-induced contraction of reservoir rock promotes fault reactivation mainly by thermal unclamping.Although cooling-induced fluid contraction and depressurization tend to stabilize the fault by increasing the effective normal stress, it may be compensated by continued fluid injection.Reservoir-scale simulation suggests that whether the thermal stress promotes or prevents the reactivation of the fault depends on the fluid flow direction, the initial stress regime, and the time as well as the location relative to the cooling zone (Jeanne et al., 2017).Apart from the limited cooling zone near the injection well (Im & Avouac, 2021;Jeanne et al., 2017), fractures and faults beyond this zone are subject to fluid pressurization at a steady-state elevated temperature, in which case the injected fluid becomes heated to the reservoir temperature and flows to fractures and faults without causing thermal stress changes.The effect of steady-state elevated temperature on injection-induced fault slip behavior may therefore be of great significance for deciphering injection-induced seismicity in geothermal systems.
Few studies have reported a pronounced effect of steady-state temperature on fault slip behavior.Raising temperature from 200°C up to 400°C has suppressed the occurrence of fast stick-slip events on dry sawcut faults in granite and gabbro (Brace & Byerlee, 1970).In contrast, the transition from creep to slow and fast earthquakes was facilitated by increasing the temperature from 25°C to 100°C on dry sawcut faults in dolostones (carbonates) (Passelègue et al., 2019).These contradictory results may imply that temperature-dependent fault slip behavior is also rock-type dependent.Moreover, injection-induced fault slip at elevated temperature is further complicated by the fluid pressure diffusion process (Ji et al., 2020;Passelègue et al., 2018;Rutter & Hackston, 2017), and thermally activated processes under thermo-hydro-mechanical (THM) conditions (e.g., KC & Ghazanfari, 2021;Blanpied et al., 1995;Rutter & Mainprice, 1978;Tenthorey et al., 2003;Yasuhara et al., 2005).Yet, to date, a systematic investigation of injection-induced fault slip in granite at different steady-state elevated temperature levels is lacking.
Here, we aim to explore experimentally the effect of steady-state elevated temperature (up to 125°C in this study) on injection-induced fault reactivation.We injected water with a similar temperature to the rock matrix into a critically stressed fault in granite and monitored the fluid pressures at the inlet and outlet boreholes, as well as the changes of shear stress and fault slip.This allowed us to identify the temperature effect on injection-induced seismicity by comparing the fault slip rate and friction coefficient upon fault reactivation.We finally provide some inferred implications for injection-induced seismicity in geothermal systems.

Materials
The experiments were performed on Odenwald granite, sourced from Rimbach, Germany.The granite contains mainly quartz, feldspar, and mica, with a mean grain size of ∼2 mm (Kluge et al., 2020).This macroscopically homogeneous granite is characterized by a porosity of ∼0.6%.The permeability of the granite was measured as ∼1 × 10 −18 m 2 at a hydrostatic confining pressure of 2 MPa and is expected to decrease further at higher effective pressures.The uniaxial compressive strength (UCS) of the granite is approximately 120-140 MPa (Blöcher et al., 2019).For this study, the cylindrical sample was 50 mm in diameter and 100 mm in length and contained a sawcut fault inclined 30° to the sample axis (Figure 1a).The sawcut fault was ground using abrasive paper with a particle size of 30.2 μm, and the two ends of the sample were ground flat and parallel within ±0.1 mm.Two small boreholes with a nominal diameter of 1.8 mm were drilled parallel to the sample axis into the fault surface near the short edges of the sample halves to facilitate pore water communication between endcaps and fault surface.In addition, two horizontal boreholes with a diameter of 2 mm were drilled to intersect the two vertical boreholes at the fault surface to accommodate thermocouples for continuous local measurements of fluid temperatures near the inlet and outlet boreholes.The thermocouples fitted tightly into the boreholes, ensuring negligible influence on the dead volume and the fluid flow pathway along the fault.The rock matrix could remain nearly intact during the experiments because of the favorable angle of the sawcut fault in the high-strength and low-permeability granite, and thus the fluid flow was constrained within the fault plane (Ji et al., 2021).

Methods
In this study, a series of triaxial shear-flow experiments on a sawcut fault in a granite sample was performed using the MTS triaxial deformation apparatus.The sample was first fully saturated at a hydrostatic confining pressure (medium: silicone oil) of 2 MPa and a pore pressure (medium: distilled water) of 0.2 MPa.Then, a sequence of four temperature steps (i.e., 22°C, 62°C, 125°C, and 24°C) were applied to the same sample, starting from room temperature (Figure 1b).Throughout the experiments, one thermocouple was placed inside the confining pressure oil and near the sample to measure the overall sample temperature, and two thermocouples were inserted into the sample to measure the fluid temperatures near the inlet and outlet boreholes (Figure S1 in Supporting Information S1).Two heater bands attached to the triaxial cell and another two cartridge heaters inserted into the baseplate were used to heat the triaxial cell assembly (Figure S2 in Supporting Information S1).We used the full power of the heating system during heating, resulting in a maximum temperature increasing rate of ∼0.0086°C/s (∼31°C/h).More details on the high-temperature system can be found in Text S1 in Supporting Information S1.The long pore pressure tube passing through the heated baseplate and the confining pressure oil (Figure S1 in Supporting Information S1) ensured that the room-temperature water had been heated to the target temperature before entering the sample.This is supported by the fact that the three thermocouples always showed similar temperature readings with a maximum difference of <6.3% throughout the entire sequence of experiments (Figure 1b), suggesting a steady-state elevated temperature with negligible thermal stress.For each temperature step, when the thermocouple readings reached the target temperature, we waited at least ∼2 hr for stabilization before conducting the experiments.
At each temperature step, a displacement-driven shear test was first conducted at a constant axial displacement rate of 1 μm/s to measure the peak shear strength (τ p ) of the fault under 21 MPa constant confining pressure and 1 MPa uniform pore pressure on the fault surface.The shear stress was then lowered to 90% of the peak shear strength by slowly retracting the axial piston.Afterward, the axial piston was fixed, and distilled water was injected via the inlet borehole at 0.2 ml/min while recording the pore pressure near the outlet borehole (constant downstream dead volume during fluid injection).The dead volumes in the up-and down-streams were ∼177 and ∼67 ml, respectively.The fluid injection was terminated when at least one full slip event was observed.The fixed axial piston during fluid injection imposed a stress relaxation condition (Rutter & Mainprice, 1978).Note that the minimum pore pressure of 1 MPa raised the phase transition (boiling) temperature of pore water to ∼180°C, suggesting that pore water remained as liquid throughout all experiments.Thus, in this study, the injection-induced fault slip was simulated at a steady-state elevated temperature beyond the limited cooling region near the injection well in EGSs (Im & Avouac, 2021).
The effective normal stress (σ′ n ) and shear stress (τ) on the fault can be calculated from the axial stress (σ 1 ), confining pressure (σ 3 ), fracture inclination angle (Ψ) with respect to sample axis and the pore pressure (P) as, The sample shortening (ΔL s ) can be obtained from the total axial displacement (ΔL) monitored by a linear variable displacement transducer (LVDT) installed outside the triaxial cell, the axial force (ΔF) measured by an in-vessel load cell, and the vertical stiffness of the testing system measured as k sys ≈ 796 kN/mm using, The fault slip displacement (ΔL f ) can therefore be estimated as, where E is the Young's modulus of the granite, and L and A are the length and cross-sectional area of the cylindrical sample, respectively.The stress, deformation, and hydraulic data were recorded at 10 Hz throughout the experiments.The sample shortening rate and fault slip rate were estimated as the derivatives of sample shortening and fault slip displacement with time at an interval of 0.1 s, respectively.The peak rates of dynamic slip events may be underestimated from the data sampled at 10 Hz (cf., McLaskey & Yamashita, 2017;Ohnaka & Shen, 1999;Passelègue et al., 2019;Xu et al., 2018), but our data allow for the comparison of relative magnitudes of peak rates.
After the experiments, we performed finite element modeling (FEM) to recover the temporal evolution of fluid pressure distribution on the fault surface during fluid injection based on the fluid pressures at the inlet (injection) and outlet (monitoring) boreholes (Text S2, Figures S3-S4, and Table S1 in Supporting Information S1).

Displacement-Driven Fault Slip
The mechanical results of triaxial shear-flow experiments at the four temperature steps are presented in Figure 2a (Temperature step I: 22°C), 2c (II: 62°C), 2e (III: 125°C), and 2g (IV: 24°C).The sample shortening calculated from eq. 3 is shown in these figures.The experiment at each temperature step contains a displacement-driven shear test and a subsequent injection-driven shear test.In the displacement-driven shear stage, stick-slip instabilities were observed at room temperature 22°C (Figure 2a) and 62°C (Figure 2c).The average static shear stress drop associated with stick-slip events reduces from ∼3.2 MPa at 22°C to ∼2.3 MPa at 62°C.When the temperature was increased to 125°C (Figure 2e), the fault exhibited stable sliding behavior.Strikingly, the stick-slip instabilities occurred again with an average static shear stress drop of ∼2.8 MPa when the temperature was reduced back to 24°C (Figure 2g).This observation suggests that an elevated temperature tends to suppress fast and unstable displacement-driven fault slip, which is consistent with the results on dry sawcut faults in granite and gabbro reported by Brace and Byerlee (1970).The primary mechanisms responsible for such transition may be related to the changing friction rate parameters (Blanpied et al., 1995(Blanpied et al., , 1998;;Scholz, 1998) and changing stiffness of the fault and the testing system with different temperatures (Passelègue et al., 2019).

Injection-Driven Fault Slip
Following each displacement-driven shear test, the shear stress was adjusted to 90% peak shear strength as measured in the displacement-driven shear test.The subsequent injection-driven shear test was conducted under a stress relaxation condition with the axial piston fixed at each temperature step.Injection-induced stable sliding was observed at room temperature 22°C (Figures 2a and 2b), but the fault showed stick-slip instabilities at higher temperatures of 62°C (Figures 2c and 2d) and 125°C (Figures 2e and 2f) with a static shear stress drop of ∼2.08 and ∼1.94 MPa, respectively.This trend suggests that elevated temperature may promote the transition of injection-induced fault slip from a slow and stable to a fast and unstable character.The injection-induced unstable slip at the final temperature step of 24°C (Figures 2g and 2h) seems not to support the trend suggested by the results from the first three temperature steps.However, unlike in the injection-induced stick-slip events at 62°C and 125°C, the injection-induced stick-slip events at 24°C were preceded by an early-onset and long-lasting slow pre-slip (see inset in Figure 2h).Examination of the fault surface showed that some larger asperities have been damaged, leading to a certain amount of gouge production (see Figure S5 in Supporting Information S1).Thus, we argue here that the injection-induced stick-slip instabilities at 24°C were results of the acceleration of the long pre-slip due to the "lubrication" of gouge (i.e., rolling on wear particles) produced after a large slip displacement of ∼1.1 mm accumulated in the previous test stages (Byerlee, 1967;Reches & Lockner, 2010).A further factor that may have led to this observation is that the effective normal stress upon injection-induced fault slip at the final temperature step of 24°C was ∼1 MPa higher than that at the first temperature step of 22°C, due to the higher resolved normal stress induced by shear hardening, which also favors unstable stick-slip behavior.More details on estimating effective normal stress are presented in Section 4.1.Therefore, slow and stable injection-induced fault slip may still occur at 24°C without gouge-induced fault lubrication and an increased effective normal stress.
Taken together, our results demonstrate that elevated temperature tends to promote the occurrence of fast and unstable injection-induced fault slip.
The peak sample shortening rate (eq.3) and fault slip rate (eq.4) during the first injection-driven slip events at different temperatures were compared (Figure 3a).Here the fault slip rate was estimated using a constant Young's modulus of granite (E = 64 GPa) measured in a dedicated triaxial compression experiment on Odenwald granite sample with strain gauges, which will cause errors of estimation due to the possible change of Young's modulus during our experiments involving repeated axial loading and unloading.The peak slip rate at the final temperature step at 24°C was the rate just before the pre-slip accelerates to become an unstable stick-slip event.It was found that the peak shortening rate and slip rate both increase with higher temperature, bearing in mind the experimental uncertainties.The perturbation force (see eq. S2 in Text S2 in Supporting Information S1) provided by the injected fluid upon fault reactivation obtained from the numerical model also shows an increasing trend with higher temperature.These results are consistent with the notion that the capability of fault rupture propagation is proportional to the magnitude of local force perturbation (Galis et al., 2015(Galis et al., , 2017)).

Fluid Pressure Distribution on the Fault
The delayed increase of the downstream monitoring pressure relative to the inlet injection pressure (Figure 2) suggests a heterogeneous fluid pressure distribution over the fault surface (Ji et al., 2020;Passelègue et al., 2018;Rutter & Hackston, 2017).We use the standard deviation of fluid pressure derived from the numerical model (Text S2 and Figure S4 in Supporting Information S1) to quantify the degree of fluid pressure heterogeneity, which decreases with higher temperature (Figure 3b), indicating that the fluid pressure distribution becomes less heterogeneous as temperature is raised from 22°C to 125°C.As a key parameter controlling the fluid pressure diffusion process, the hydraulic diffusivity D is given as D = k/μs, where k, μ, and s are permeability, fluid viscosity, and storage capacity, respectively.The water viscosity reduces by ∼4 times from room temperature to 125°C, leading to the increase of time-weighted average hydraulic diffusivity D a by ∼3 times (see Table S1 in Supporting Information S1) with some influences from temperature-dependent and slip-dependent fault permeability and storage capacity.The curve for the last temperature step at 24°C is shown as a blue dashed line for reference.The degree of fluid pressure heterogeneity in this case is larger than the case at 125°C but smaller than at 22°C and 62°C, indicating that the fault surface roughness has experienced irreversible changes after the ∼1.1 mm cumulative slip displacement in the previous test stages (see Figure S5 in Supporting Information S1).These results suggest that temperature has a primary control on the fluid pressure distribution over the fault surface mainly by changing the fluid viscosity, which may in turn modulate the fault slip behavior.

Competition Between Thermally Activated Processes Affecting Fault Friction
The reason why temperature seems to promote the slow-to-fast transition of injection-induced fault slip may be explored by investigating the evolution of the friction coefficient upon approaching failure.In Figure 4a, the shear stress is shown as a function of effective normal stress during the displacement-driven and injection-driven shear tests at each temperature step.The effective normal stress during injection-driven shear tests was estimated by subtracting the average fluid pressure across the fault surface as estimated from the numerical model (Text S2 and Figure S4 in Supporting Information S1) from the normal stress (eq. 1) on the fault.The friction coefficients upon displacement-driven failure and injection-driven failure are generally compatible with Byerlee's rule for rock friction (Byerlee, 1978) generalized from a large amount of displacement-driven shear tests (see gray dash lines in Figure 4a).
The friction coefficient is plotted in Figure 4b as a function of temperature.The displacement-driven peak friction μ p increases with temperature steps from I (22°C) to III (125°C), primarily caused by the shear hardening associated with cumulative slip displacement (e.g., Ji & Wu, 2020;Noël et al., 2019;Tembe et al., 2010).However, this may also imply that the friction coefficient of granite may be relatively independent of temperature, at least within the temperature range explored in this study, which is consistent with the results reported by Stesky et al. (1974) on sawcut faults in Westerly granite up to 500°C.It is noteworthy that the displacement-driven peak friction μ p becomes lower at the final temperature step of 24°C, mostly because gouge has been produced after the ∼1.1 mm long cumulative fault slip as inferred from the topographic changes of the fault surface (Figure S5 in Supporting Information S1) and thus the fault has been weakened slightly by rolling on wear particles (Byerlee, 1967).Injection-driven reactivation friction μ r is always lower than the respective displacement-driven peak friction μ p , but also increases with temperature (Figure 4b).The always-lower injection-driven reactivation The ratio between injection-driven reactivation friction μ r and displacement-driven peak friction μ p was calculated, and it increases with higher temperature from 94.0% at 22°C up to 99.4% at 125°C (Figure 4b), indicating a thermally enhanced process has operated which can increase the fault friction in a temperature-dependent and/ or time-dependent fashion.Such "fault healing" (e.g., Marone, 1998;Marone et al., 1995;Olsen et al., 1998;Rutter & Maddock, 1992;Tenthorey et al., 2003;Yasuhara et al., 2005) due to temperature-mediated and/or time-mediated processes under thermo-hydro-mechanical conditions can partially compensate for the reduction in fault friction associated with stress relaxation, which is also a thermally activated process but likely characterized by a different Arrhenius rate constant.The ratio μ r /μ p is always lower than 100% in our study, indicating that the friction reduction dominates the competition with fault healing under the stress relaxation experimental condition in the hydrothermal environment of the present tests.In addition, the injection time required before the onset of fault reactivation is also longer at higher temperature (Table S1 in Supporting Information S1).That is, enhanced fault healing induced by accelerated thermally activated processes at higher temperature with longer injection time increases the ratio μ r /μ p , which in turn tends to increase the perturbation force from the injected fluid required for reactivation and thus increases the fault slip rate upon failure (Im et al., 2017).
Although not specifically explored experimentally in the present study, thermally activated processes causing fault healing are expected to include enhanced dissolution and precipitation of feldspar and quartz in the hydrothermal environment and the resulting cementation-welding of contact area at elevated temperature (KC & Ghazanfari, 2021;Yasuhara et al., 2005), development of adhesion across surfaces through precipitation of minerals that are products of low-grade metamorphic reactions, and diffusive adhesion at asperity tips across surfaces (McLaskey et al., 2012).Thermally activated stress relaxation processes may include pressure-solution slip (Rutter & Mainprice, 1978), sub-critical microcrack growth (Atkinson & Meredith, 1987), and transient or anelastic intracrystalline-plastic creep (Carter & Kirby, 1978).The detailed thermally activated processes operating in injection-induced slip of critically stressed faults at steady-state elevated temperatures merit further studies.

Implications for Injection-Induced Seismicity in Geothermal Reservoirs
We have here experimentally demonstrated that elevated temperature may promote fast and unstable injection-induced fault slip by accelerating hydrothermal reactions and enhancing fault healing, in the same way that time in the "hold" period of slide-hold-slide tests can do the same thing (e.g., Marone, 1998;Marone et al., 1995).Our experiments provide complementary insights into the mechanisms of injection-induced seismicity, particularly for the high-temperature effect.Although extrapolation of our experimental findings to higher temperatures and different rock types would be presently too ambitious, these results may partially explain the causal link between higher reservoir temperature and larger maximum magnitude of injection-induced seismic events in various types of geothermal systems with different reservoir rocks, as summarized by Buijze et al. (2019) (Figure S6 in Supporting Information S1).
These results may also provide a plausible explanation for the observation in Basel EGS that larger magnitude post-shut-in seismic events concentrate near the deeper part of reservoir (Figure S7 in Supporting Information S1).Pore pressure migration, as a well-established and accepted mechanism, can only explain why shut-in seismic events appear near the periphery of the seismic cloud (Mukuhira et al., 2016).In terms of the larger magnitude of post-shut-in seismic events near the deeper part, first, it is true that a deeper depth normally means a higher mean pressure and a higher differential stress, requiring a larger pore pressure to reactivate the fault to slip and hence higher local seismic magnitudes.Second, a larger section of the fault may have been induced to slip due to the more uniform pore pressure distribution at the edge of the seismic zone after shut-in (Mukuhira et al., 2016).Third, higher temperatures will raise the pore pressure of injected fluid as they penetrate into the deeper hot zone, leading to thermal pressurization and increase the seismic hazards.In addition to these factors, considering the average temperature gradient of ∼40°C/km at Basel EGS (Ladner & Häring, 2009), the temperature difference can reach ∼40°C between the top (∼3,800 m) and the bottom (∼4,800 m) of the seismic cloud (Figure S7 in Supporting Information S1).Therefore, we may argue from the present experiments that even under otherwise similar conditions, the higher temperature at the deeper part of reservoir could promote the occurrence of faster fault slip and larger seismic events once the pore pressure migrates there after the termination of fluid injection.
Our results are derived from one suite of experiments on a centimeter-scale sawcut fault in granite within a limited temperature range up to 125°C, which may restrict the confident extrapolation of the findings to other rock types and higher temperatures.In future, we see a further necessity to explore temperature effects on injection-induced fault slip with a wider range of parameters on more rock types.

Conclusions
We performed a series of triaxial shear-flow experiments on a sawcut fault in granite at four temperature steps (i.e., 22°C, 62°C, 125°C, and 24°C) to simulate injection-induced fault slip at steady-state elevated temperatures.
Local temperature measurements showed that there was negligible temperature difference between the injected fluid and the rest of the sample, since the fluid flows through the heated pore pressure tube, suggesting that injection-induced fault slip was stimulated at a region beyond the limited cooling zone of any thermal stress effect near the injection well.The results showed that the fluid pressure distribution across the fault surface becomes more uniform at higher temperatures, primarily due to the reduced water (injection fluid) viscosity.Injection-induced fault slip became faster at higher temperatures, consistent with the increasing perturbation force provided by the injected fluid.A competition developed between thermally activated stress relaxation (friction reduction) and fault healing (friction increase) processes under a stress relaxation condition in the hydrothermal environment.The fault healing partially compensated for the friction reduction under the stress relaxation experimental condition.Elevated temperature was inferred to enhance fault healing and thus to promote a faster slip rate upon eventual injection-induced fault reactivation.These results demonstrate a temperature effect on injection-induced seismicity, which might partly explain: (a) the trend summarized from numerous geothermal sites that the maximum magnitude of injection-induced seismic events increases with higher reservoir temperature, and (b) the observation that larger post-shut-in seismic events concentrate near the deeper part of geothermal reservoir such as in the Basel EGS.

Figure 1 .
Figure 1.Sample geometry and temperature steps.(a) Schematic drawing of the sample assembly with inlet and outlet boreholes and two horizontal boreholes accommodating thermocouples.(b) Four temperature steps applied in this study.The duration of displacement-driven (dis) and injection-driven (inj) shear tests at each temperature step are normalized by the total experimental time at the respective temperature step.

Figure 2 .
Figure 2. Time history of shear stress, fluid pressure (injection and monitoring pressures) as well as sample shortening during the triaxial shear-flow experiments, consisting of a displacement-driven shear test and a subsequent injection-driven shear test, at (a) Temperature step I: 22°C, (c) Temperature step II: 62°C, (e) Temperature step III: 125°C, and (g) Temperature step IV: 24°C.Enlargement of the first injection-induced slip event in each temperature step is shown correspondingly in the right column: (b) Temperature step I: 22°C, (d) Temperature step II: 62°C, (f) Temperature step III: 125°C and (h) Temperature step IV: 24°C.In addition to the parameters shown in the left column, the sample shortening rate is shown in the right-panel figures to illustrate better the slip characteristics.The inset in (h) shows the early-onset and long-lasting slow stable pre-slip before the first injection-induced dynamic slip event at 24°C.Note different scales of sample shortening and sample shortening rate in the right panel.The shortening rate in (b) and the inset in (h), and the sample shortening in the inset in (h) have been smoothed by applying a Savitzky-Golay filter to remove high-frequency noise.τ p is the peak shear strength denoted by 5-pointed red stars.

Figure 3 .
Figure 3. (a) Peak shortening rate and slip rate as well as perturbation force upon fault failure as a function of temperature.The open data points show the results at the last temperature step of 24°C.Note that only the results for the first event at each temperature step are shown, because they occur under similar stress conditions.(b) Temporal evolution of the standard deviation of fluid pressure, which quantifies the degree of fluid pressure heterogeneity, during fluid injection at four temperature steps.

Figure 4 .
Figure 4. (a) Shear stress as a function of effective normal stress during the displacement-driven shear test and a subsequent injection-driven shear test at the four temperature steps.The four 5-pointed red stars represent the peak shear strengths obtained in the displacement-driven shear tests.The gray squares represent the shear stress upon injection-induced fault reactivation.(b) Friction coefficient and friction ratio of the injection-driven reactivation friction to displacement-driven peak friction as a function of temperature.The open data points show the results at the last temperature step of 24°C.