# Single-Asperity Friction and Wear in Seismic Faults: 1. Experiments on Marble

Clerc A., Guilhem Mollon, Amandine Ferrieux, L. Lafarge, Aurélien Saulot, D. Deldique, Alexandre Schubnel, Laetitia Vieille

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## To cite this version:

Clerc A., Guilhem Mollon, Amandine Ferrieux, L. Lafarge, Aurélien Saulot, et al., Single-Asperity Friction and Wear in Seismic Faults: 1. Experiments on Marble. Journal of Geophysical Research: Solid Earth, 2025, 130 (7), pp.e2025JB031344. 10.1029/2025JB031344. emse-05189748

HAL Id: emse-05189748

https://hal-emse.ccsd.cnrs.fr/emse-05189748v1

Submitted on 28 Jul 2025

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Distributed under a Creative Commons Attribution 4.0 International License
# JGR Solid Earth

## RESEARCH ARTICLE

10.1029/2025JB031344

**Key Points:**

* A novel experimental device is presented, which mimics the friction and wear of a single fault asperity in coseismic conditions

* Interface evolves in a repeatable way during sliding following three successive regimes, with increasing friction and wear rate

* The presence of a geometrical asperity does not preclude the existence of a persistent gouge layer, especially in a mature sliding regime

**Supporting Information:**

Supporting Information may be found in the online version of this article.

**Correspondence to:**

G. Mollon,
guilhem.mollon@insa-lyon.fr

**Citation:**

Clerc, A., Mollon, G., Ferrieux, A., Lafarge, L., Saulot, A., Deldique, D., et al. (2025). Single-asperity friction and wear in seismic faults: 1. Experiments on marble. *Journal of Geophysical Research: Solid Earth, 130*, e2025JB031344. https://doi.org/10.1029/2025JB031344

Received 13 FEB 2025
Accepted 7 JUL 2025

**Author Contributions:**

**Conceptualization:** G. Mollon

**Funding acquisition:** G. Mollon

**Investigation:** A. Clerc

**Methodology:** G. Mollon, A. Ferrieux, L. Lafarge, A. Saulot, L. Vieille

**Resources:** A. Clerc

**Supervision:** G. Mollon

**Visualization:** D. Deldique, A. Schubnel

**Writing – original draft:** A. Clerc, G. Mollon

**Writing – review & editing:** G. Mollon, A. Ferrieux, L. Lafarge, A. Saulot, D. Deldique, A. Schubnel, L. Vieille

© 2025. The Author(s).
This is an open access article under the
terms of the Creative Commons
Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.

<figure><img src="image_3.png" /></figure>

## Single-Asperity Friction and Wear in Seismic Faults: 1. Experiments on Marble

A. Clerc¹, G. Mollon¹ ID, A. Ferrieux¹ ID, L. Lafarge¹, A. Saulot¹, D. Deldique², A. Schubnel² ID, and L. Vieille³

¹INSA Lyon, CNRS, LaMCoS, Villeurbanne, France, ²Laboratoire de Géologie, Ecole Normale Supérieure/CNRS UMR 8538, PSL University, Paris, France, ³Mines Saint-Etienne, Université Lyon, CNRS, UMR 5307 LGF, Centre SPIN, Saint-Etienne, France

**Abstract** Common representations of seismic faults often fall into two categories. Either the model focuses on clean rough surfaces in sliding contact, or the model focuses on the gouge production and shearing between two smooth surfaces. In this work, we wish to reconcile these two main models by using tribological tools and concepts, in order to pave the way for a more accurate model of geometrically complex faults. A pin-on-disc experimental device is employed to investigate the response of a single asperity to shear sliding, in presence of granular gouge. Near co-seismic conditions are applied on Carrara marble samples (contact stress, contact area, sliding velocity) and real time acquisition sensors as well as post-mortem analyses on the contact surfaces provide qualitative and quantitative information on the frictional behavior of the downscaled lab fault. The results for moderate sliding velocity (0.01 m s⁻¹) tests show a complex behavior. Three regimes are underlined, which highlights the interplay between granular gouge and asperities. The last regime is seen as a steady state with rough contact surfaces and the presence of a granular gouge layer. This observation leads to the conclusion that in a model for geometrically complex fault, granular gouge and asperities are not self-excluding and should be considered together. This work is complemented by a numerical model presented in a companion paper.

**Plain Language Summary** In this work, we present a novel experimental device designed to mimic a small portion of a seismic fault during an earthquake. More specifically, we simulate an asperity, that is, a geometrical feature that concentrates the load received by the fault, and is therefore pivotal to understand its behavior. This device is applied to Carrara marble, and the experimental results show a systematic evolution of the contact interface below the asperity, from a clean and smooth contact with low wear and low friction, to a rough contact covered with rock powder with high friction and wear. Surface observations and characterizations allow to derive local scenarios for the different sliding regimes, and provide a new understanding on the evolution of faults in the presence of geometrical complexity and rock powder production by severe wear.

## 1. Introduction

In order for earthquakes to propagate, the friction force opposing the relative motion of the two walls of a fault needs to diminish during this motion. Finding the reasons and a predictive model for this weakening is one of the most important challenges of modern earthquakes physics. When it comes to conceptualizing seismic faults, two opposite views are commonly encountered:

1. In the first representation (Figure 1a), seismic faults are seen as the interface between two surfaces of bare rock, with a roughness extending at all scales (Candela et al., 2012). These surfaces interact mechanically through a certain number of geometrical asperities which constitute the real contact area (Dieterich & Kilgore, 1994). Since this real contact area is orders of magnitude smaller than the nominal one, asperities are submitted to very large normal and tangential stresses. This representation is at the basis of the flash heating theory (Rice, 2006; Hayward et al., 2019), which states that slip-weakening is related to quasi-adiabatic heating and subsequent weakening/melting of fault asperities. Combined with probabilistic arguments, this representation is also at the core of the classical wear model proposed in (Archard, 1953), which was later enriched by (Queener et al., 1965) and by (Wang & Scholz, 1994). When adopting this view, attention is paid on the statistics of the asperities population in the fault plane (Greenwood & Williamson, 1966). Asperities and geometrical complexities have been studied in the field (Kirkpatrick et al., 2020; Little et al., 2025; Sammis et al., 1999), in the lab (Barbery et al., 2023; Dieterich & Kilgore, 1994; Hayward et al., 2019; Selvadurai & Glaser, 2017) and in simulations (Asadi et al., 2012; Aghababaei et al., 2018; Little et al., 2025), and were
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Different models of a seismic fault. (a) Two clean and rough surfaces in contact through a series of asperities; (b) two planar surfaces separated by a granular gouge; (c) a combination of the two previous models; (d) a laboratory proxy of this combined model.</figcaption></figure>

found to be persistent along several sliding events (Aubry et al., 2018; Barbery et al., 2021; Mollon et al., 2024; Schmittbuhl et al., 2006). Following this model, faults are thus considered as 2D objects, since their thickness is disregarded.

2. In the second representation (Figure 1b), seismic faults are seen as mathematical planes separated by a certain thickness of granular gouge created by abrasive wear of the surfaces during previous slips (Robertson, 1983; Shimamoto & Logan, 1981; Scholz, 1987; Wallace & Morris, 1986). This view is analogous to the tribological “third body” theory (Godet, 1984), and is supported by field observations and experimental evidences of gouge creation in rotary shear (Reches & Lockner, 2010) and triaxial (Aubry et al., 2018) experiments. It is convenient to adopt this perspective when weakening phenomena within the gouge (e.g., distributed or localized shearing (Andò et al., 2012), fabric evolution (Scuderi et al., 2017; Casas et al., 2023), comminution (Reches & Lockner, 2010), thermal pressurization (Rice, 2006), fluid flows, heat creation and diffusion (Di Toro et al., 2011), pervasive melting (Nielsen et al., 2008; Goldsby & Tullis, 2011; Mollon et al., 2021), etc.) are to be spatially resolved in the direction orthogonal to the fault plane. Variations along this plane are then ignored, as well as fault roughness, and faults are mostly seen as 1D objects.

Both models are firmly established based on observations (fault geometrical complexity in the first case, pervasive gouge layers in the second), and yet they disagree on the way faults should be conceptualized. The fault mechanics community is very aware that real faults are more complex, but authors nevertheless have to adopt one view or the other depending on their needs. These two models are indeed difficult to unify, and yet such a unification is necessary in order to understand the physics of fault friction. Their limitations are very clear: the first one disregards the effect of the gouge and relies on simplistic models of asperities, with limited experimental validation; the second one ignores any geometrical and mechanical effect of fault surface irregularities and often relies on unsatisfactory granular rheology. There is a need to reconcile these two representations, by investigating how gouge layers and geometrical asperities interact during sliding (Figure 1c). This relation was already questioned in the literature. Among various examples (Brodsky et al., 2011), showed in a field study that the linear increase in gouge thickness and the power-law decrease in roughness with slip distance could only be explained by a re-roughening process by brittle wear, and (Mollon et al., 2024) showed numerically that persistent asperities (identified as stress concentrations on the fault walls) spontaneously develop even in the presence of a well-established gouge layer. This is, however, one of the topics where earthquake science can benefit the most from the tools and concepts of engineering tribology. The concept of a third body, that is, of a layer of solid matter trapped in the interface and controlling friction, was first proposed in (Godet, 1984) and enriched in (Bertzier, 1990). This layer has been the topic of countless research works for all classes of materials, both in the lab and in simulations (Bouillanne et al., 2024; Fillot et al., 2007; Österle & Urban, 2006; Rigney & Hammerberg, 1998; Pham-Ba & Molinari, 2021; Quacquarelli et al., 2023; Stoyanov et al., 2013; Zhang et al., 2020). Meanwhile, single-asperity lab tests were initiated with the scratch-tests of (Tabor, 1954), and have now become common tribological practice (Bouchot et al., 2024; Colas et al., 2013; Engelder & Scholz, 1976; Gotsmann & Lantz, 2008; Hsia et al., 2020; Jaza et al., 2021; Mekicha et al., 2021). In most cases, third body is present in these experiments,
<figure><img src="image_5.png" /><figcaption>**Figure 2.** (a) Sketch of the experimental bench; (b) Photos of an intact (left) and a worn (right) disc on the plateau; (c) Photo of a new pin, in the pin holder and a worn pin, beheaded by the sliding test.</figcaption></figure>

and takes an active part in the tribological response. Simulations showed that the roughness of three-body contacts is governed by the third body interactions with the worn surfaces and by successive episodes of brittle and ductile adhesive wear (Milanese et al., 2019). The presence or absence of a third body in friction asperity contacts can lead to widely varying friction and wear behaviors (Hsia et al., 2020). The third body can keep its tribological properties when transported from a contact to another, including its rate-dependant response (Ciprari et al., 2023). In the present work, we take advantage of this tribological heritage to run single asperity friction and wear tests on marble samples, as a proxy to the sliding of rough faults in coseismic conditions (Figure 1d). This allows to investigate the interactions between an asperity and a gouge layer, and to pave the way to a more unified tribological model in geometrically complex faults (Figure 1c).

## 2. Methods

### 2.1. Experimental Apparatus

In order to study the evolution of friction and wear under co-seismic conditions, we borrow from the tribological practice the pin-on-disc experiment (Figure 2). In this type of experiment, we downscale a fault to a single asperity of one side of a fault (represented by the pin) in sliding contact with the other side of the fault (the disc). Our TriboRock apparatus consists in a rotating plateau bearing the rock disc and a pin holder, fixed on an axis, on which a vertical dead load is applied (Figure 2a). The rotating plateau is animated by a motor which allows a rotation with a large range of angular velocities. The linear velocity is a function of the track radius and ranges from lower than 0.01 m s⁻¹ up to above 1 m s⁻¹. A second motor allows the pin holder to translate on the disc, in order to prescribe a track radius before the test or to control it during the test, allowing for example, spiral trajectories. Both motors are controlled through a Motion Perfect (TrioMotion) interface.

There are different sensors monitoring the good process of the experimental test. A piezoelectric triaxial force detector (from Kistler) on the pin holder tracks the evolution of the forces in the three directions of space (Figure 2a). The normal force being applied through a dead load, the measurement of the actual vertical force allows to quantify (a) possible inertial effects in the vertical direction and (b) sensor drift. The shear forces in the direction of the sliding track are measured in order to access to the friction coefficient, and the shear measurement orthogonal to the track provides a verification of sensor alignment. An eddy current sensor measures the distance between the pin holder and the disc, and gives access to the total wear of the pin-track couple (pin height lost, abrasive digging of the track and deposition of third body if any). A DEWESoft data acquisition software collects the data from these detectors at a given frequency (depending on the linear velocity applied).
It was chosen to conduct the experimental test on Bianco Carrara Marble (from Carrara, Italy in the Apuan Alps). This metamorphic rock is a standard of rock mechanics, and has been the topic of many experimental studies relevant to earthquake science (Aubry et al., 2020; Boneh et al., 2013; Carpenter et al., 2016; Han et al., 2010; Niu et al., 2024; Pozzi et al., 2018; Park et al., 2021; Ree et al., 2014; Siman-Tov et al., 2015; Smith et al., 2015; Tesei et al., 2014; Verberne et al., 2014; Yao et al., 2016). It is mainly composed of calcite grains (more than 98%, 150 µm average grain size) with very few grains of quartz, pyrite and epidote in the veins (few microns average grain size) (Fredrich et al., 1989; Aubry et al., 2020). From one Carrara Marble block, discs and pins are machined according to the designs given in Figure S1 in Supporting Information S1. The disc is fixed on the rotating plateau by a bolted joint at its center, and clamped at two extremities of its diameter (Figure 2b). The pin is a cylinder with a semi-spherical head (Figure 2c) of 10 mm diameter. Despite the large ratio length/radius, the pin is well held in a pin holder during the test, which prevents it from vibrating or breaking while being sheared (Figure 2c). The discs are water-jet cut up from a block of Carrara Marble. Their surfaces are then prepared with successive application of diamond grinders of different sizes (from 36 mm up to 320 mm) and with a last application of a polyester sheet to eliminate the traces left by the grinder and homogenize the surface. The final discs present absolute surface roughness of $R_a \approx 1.1$ µm and a root mean square (RMS) roughness of $R_q \approx 1.8$ µm. The discs can be considered as smooth based on the terminology used in (Aubry et al. (2020)). On the other hand, the pins come from the core sampling of the same block of Carrara Marble with a diamond drill bit. The final diameter of the cylinder and the half sphere are made with a diamond grinder. All the processes are done in presence of water, in order to eliminate fine powders and mud, and in order to prevent the disc temperature from rising.

## 2.2. Frictional Test Process

The principle of a pin-on-disc tribometer is rather simple. The radius of the track, the sliding distance and the velocity are chosen before the beginning of the test, and implemented in the Motion Perfect interface. Using the horizontal motor, the pin is first translated at the chosen radius $R_{\text{track}}$ on the disc, which corresponds to a circular sliding track with a period $L_{\text{track}}$. It is then lowered and put in contact with the disc. Once the dead load is applied on the top of the pin trolley (configuration of Figure 2), the disc starts to move, rotating thanks to the rotational motor. The acceleration is calibrated to last one second (as is the deceleration at the end of the test). The total sliding distance is called $d$. In the present study, if not stated otherwise, tests are performed with a linear velocity of 0.01 m s⁻¹, under a normal load of 100 N, and data are recorded at the sampling rate of 1,000 Hz. Table 1 references all the tests. In this experimental campaign, four discs and 18 pins have been used (plus three pins used for the repeatability tests), with the same initial surface states. These elements are used to provide a consistent catalog of experimental tests and ensure repeatability (See Figure S2 in Supporting Information S1).

# 3. Results

## 3.1. Friction and Wear

The data collected during experimental tests have to be filtered and processed before being analyzed. Figure 3 illustrates how the tests data are pre-processed, based on the MT024 test. This test uses a radius of $R_{\text{track}} = 6$ cm, with a load of 100 N, a velocity of 0.01 m s⁻¹, and a sliding distance $d = 34$ m (see Table 1). Raw effective friction and wear signals are first plotted against time (Figure 3a). As this figure illustrates, the friction signal is subjected to an important variability, essentially because the pin travels a long distance and meets regions of the track with spatially varying states. A filtered friction coefficient is computed from the ratio between the shear force ($F_x$, tangent to the track and to the sliding) and the normal force ($F_z$), smoothed though a gaussian filter with $\sigma = l_{\text{filter}} / \Delta t$, where $l_{\text{filter}} = 500$ µm is the characteristic filtering length, $v = 0.01$ m s⁻¹ is the linear velocity used for all tests and $\Delta t = 10^{-3}$ s is the period of data acquisition. This filtering, which is illustrated in the insert of Figure 3a, is calibrated to remove most of the high-frequency fluctuations while keeping the general friction evolution along the pin trajectory. The raw wear signal expresses the vertical lowering of the pin's trolley. On the zoom in the lower green box in Figure 3a, the component of the wear signal linked to the defaults in disc planarity and alignment is noticeable (see dotted vertical lines). The track slope associated with this planarity default remains lower than 1 mm/m, and is not expected to affect our measurements. Its effect on the signal is corrected based on the vertical motion measured during the first lap, where wear is negligible, and allows to compute a wear increment (i.e., the amount of height loss at a given location on the disc in one lap). By considering the linear velocity, the length of a lap and the sampling frequency, maps of both (respectively filtered and corrected)
<table><caption>**Table 1**

Parameters of the Experimental Tests</caption><thead><tr><th rowspan="2">Name</th><th rowspan="2">Disc</th><th rowspan="2">Pin</th><th rowspan="2">Slip rate (m.s<sup>-1</sup>)</th><th rowspan="2">Radius (m)</th><th rowspan="2">Normal force (N)</th><th rowspan="2">Sliding distance (m)</th><th colspan="2">Run-in period</th><th colspan="2">Transition zone</th><th colspan="2">Mature regime</th><th rowspan="2">Remarks</th></tr><tr><th>Wear rate (*10<sup>-6</sup>)</th><th>SD</th><th>Begin (m)</th><th>Wear rate (*10<sup>-6</sup>)</th><th>SD</th><th>Begin (m)</th><th>Wear rate (*10<sup>-6</sup>)</th><th>SD</th></tr></thead><tbody><tr><td>MT013</td><td>DMR02</td><td>PM013</td><td>0.01</td><td>5*10<sup>-2</sup></td><td>100</td><td>10</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>No wear measure</td></tr><tr><td>MT015</td><td>DMR02</td><td>PM015</td><td>0.01</td><td>9*10<sup>-2</sup></td><td>100</td><td>10</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>No wear measure</td></tr><tr><td>MT019</td><td>DMR02</td><td>PM019</td><td>0.01</td><td>10*10<sup>-2</sup></td><td>100</td><td>10</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>MT020</td><td>DMR04</td><td>PM020</td><td>0.01</td><td>10*10<sup>-2</sup></td><td>100</td><td>10</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>Stop every 1 m</td></tr><tr><td>MT021</td><td>DMR02</td><td>PM021</td><td>0.01</td><td>8*10<sup>-2</sup></td><td>100</td><td>25</td><td>21.16</td><td>21.86</td><td>24.12</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>MT022</td><td>DMR04</td><td>PM022</td><td>0.01</td><td>8*10<sup>-2</sup></td><td>100</td><td>25</td><td>34.09</td><td>28.90</td><td>17</td><td>...</td><td>...</td><td>...</td><td>...</td><td>Stops every 1 m</td></tr><tr><td>MT023</td><td>DMR02</td><td>PM023</td><td>0.01</td><td>12*10<sup>-2</sup></td><td>100</td><td>60</td><td>...</td><td>...</td><td>59.56</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>MT024</td><td>DMR02</td><td>PM024</td><td>0.01</td><td>6*10<sup>-2</sup></td><td>100</td><td>35</td><td>58.69</td><td>48.43</td><td>4.15</td><td>128.10</td><td>23.03</td><td>28.65</td><td>202.28</td><td>26.29</td></tr><tr><td>MT026</td><td>DMR03</td><td>PM026</td><td>0.01</td><td>6*10<sup>-2</sup></td><td>100</td><td>50</td><td>...</td><td>...</td><td>10.56</td><td>76.02</td><td>26.34</td><td>47.12</td><td>123.00</td><td>4.61</td><td>No wear measure at the beginning</td></tr><tr><td>MT027</td><td>DMR04</td><td>PM027</td><td>0.01</td><td>13*10<sup>-2</sup></td><td>200</td><td>60</td><td>...</td><td>...</td><td>59.63</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>MT029</td><td>DMR03</td><td>PM029</td><td>0.01</td><td>10*10<sup>-2</sup></td><td>100</td><td>60</td><td>37.60</td><td>33.31</td><td>6.90</td><td>69.71</td><td>14.14</td><td>37.07</td><td>73.34</td><td>9.7</td></tr><tr><td>MT030</td><td>DMR03</td><td>PM030</td><td>0.01</td><td>7.5*10<sup>-2</sup></td><td>100</td><td>50</td><td>49.07</td><td>52.34</td><td>4.71</td><td>91.13</td><td>28.78</td><td>24.50</td><td>102.21</td><td>22.61</td></tr><tr><td>MT031</td><td>DMR03</td><td>PM031</td><td>0.01</td><td>10*10<sup>-2</sup></td><td>100</td><td>40</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>MT032</td><td>DMR03</td><td>PM029</td><td>0.01</td><td>13*10<sup>-2</sup></td><td>100</td><td>60</td><td>5.30</td><td>3.99</td><td>6.53</td><td>39.28</td><td>8.68</td><td>42.47</td><td>62.44</td><td>8.86</td></tr><tr><td>MT033</td><td>DMR03</td><td>PM030</td><td>0.01</td><td>7.5*10<sup>-2</sup></td><td>100</td><td>40</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>MT034</td><td>DMR05</td><td>PM034</td><td>0.01</td><td>5*10<sup>-2</sup></td><td>100</td><td>40</td><td>20.06</td><td>26.41</td><td>8.17</td><td>102.28</td><td>26.02</td><td>42.75</td><td>118.59</td><td>8.52</td></tr><tr><td>MT035</td><td>DMR05</td><td>PM035</td><td>0.01</td><td>6*10<sup>-2</sup></td><td>100</td><td>45</td><td>27.76</td><td>28.94</td><td>4.90</td><td>54.75</td><td>11.92</td><td>30.53</td><td>109.20</td><td>11.60</td></tr><tr><td>MT036</td><td>DMR05</td><td>PM036</td><td>0.01</td><td>11*10<sup>-2</sup></td><td>200</td><td>32</td><td>-0.01</td><td>0.07</td><td>8.98</td><td>195.70</td><td>73.8</td><td>28.34</td><td>306.16</td><td>38.74</td><td>No wear measure at the beginning</td></tr><tr><td>MT037</td><td>DMR05</td><td>PM037</td><td>0.01</td><td>12*10<sup>-2</sup></td><td>100</td><td>90</td><td>16.16</td><td>13.07</td><td>27.14</td><td>54.75</td><td>11.91</td><td>88.68</td><td>109.20</td><td>11.60</td></tr><tr><td>MT038</td><td>DMR05</td><td>PM038</td><td>0.01</td><td>13*10<sup>-2</sup></td><td>100</td><td>110</td><td>18.94</td><td>16.07</td><td>56.36</td><td>64.78</td><td>9.89</td><td>...</td><td>...</td><td>...</td></tr></tbody></table>

quantities can be drawn in space and time (Figures 3b and 3c). In Figure 3b, friction variations can be observed both in the vertical and in the horizontal directions: horizontal patterns are mostly associated to the state of the pin, while vertical patterns are mostly associated to the state of the disc. For example, on the 30th lap, some local event in the interface associated with the pin reduced the friction coefficient and lasted less than one entire lap. Conversely, between the 180° and 225° positions, one can notice a slight increase in the friction coefficient that lasts during the entire experiment. This heterogeneity is thus linked to the disc's surface. Wear measure also exhibits such variations (Figure 3c), although most of the recorded height loss is associated to the pin, which wears continuously. On the 30th lap, there is a decrease of wear (low wear increment compared to the preceding and following laps), simultaneously to a temporary reduction of friction. For both quantities, an averaged value for each lap can be deduced from these maps, giving the averaged friction coefficient and averaged wear against the lap number, which can be also converted in cumulated wear (Figure 3d). The overall protocol is applied to the data from all experiments.

The evolution of the lap-averaged friction coefficient as a function of the sliding distance is presented in Figure 4 for various values of $R_{track}$. For small distances (below 10 m; Figure 4a) the lap-averaged friction coefficient increases steadily from an initial value of ~0.12–0.15, until reaching a local peak close to 0.2 and decreasing again during a few laps. From thereon, friction steadily increases until reaching a plateau at ~0.65–0.75 (Figure 4b), in agreement with typical values from the literature (Han et al., 2010). Another important observation from Figure 4c is that the kinetics of the lap-averaged friction evolution depend on the radius chosen for the track (also see Table 1). In a first approximation, Figure 4c shows that the smaller the radius, the faster the high value plateau is reached. The tests with the largest radii (12 and 13 cm respectively) do not reach the plateau even after 100 m of
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Post-processing of friction and wear data of the MT024 test ($R_{track}$ = 6 cm, $d$ = 34 m). (a) Raw data of friction coefficient and wear measurements against time with zooms in green inserts illustrating raw friction filtering and periodic geometrical effects in the raw wear measurements; (b) Friction coefficient map as a function of the angular position of the pin on the disc of the lap number; (c) Wear increment map as a function of the angular position of the pin on the disc and of the lap number; (d) Lap-averaged friction coefficient and cumulated wear against lap number and distance.</figcaption></figure>

sliding. It indicates that, in addition to the evolution of the state of the pin, track evolution (controlled by the frequency of passage of the pin at each location, hence by the track radius) also control system kinetics.

This friction evolution for low-speed tests can be interpreted as the succession of three regimes (Figure 5a). The first regime, which consists in the moderate initial increase of the averaged friction coefficient can be interpreted

<figure><img src="image_7.png" /><figcaption>**Figure 4.** Friction curves of the different experimental tests against the sliding distance. Data points correspond to lap-averaged friction coefficients. (a) For small sliding distances, the friction coefficient stays under 0.3 and evolves according to the radius of the track. (b) For longer sliding distances, the friction coefficient increases until reaching a plateau around 0.7. (c) Same graph than (b) but with larger track radii data (0.12 and 0.13 m) which show slower kinetics than for smaller track radii.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Definition and characteristics of the different regimes during an experimental test. (a) Definition of the different regimes: run-in period, transition zone, mature regime according to the standard deviation of the friction coefficient (MT024 test taken as an example); (b) Evolution of the wear rate during the three stages; (c) Starting point of the transition zone (in blue, left axis) and of the mature regime (in red, right axis) according to different track radii (MT024, MT029, MT030, MT037, and MT038 tests); (d) Wear rate and its standard deviation calculated for the different regimes, for different track radii (data points for a given radius were slightly shifted horizontally to ease reading).</figcaption></figure>

as a run-in regime (Blau, 2005). During this regime, the friction increases smoothly, as well as its variability during a given lap. This indicates that both surfaces are still clean and smooth, but start to slowly evolve and degrade. This regime ends when the standard deviation of the friction coefficient during a lap decreases for the first time (Figure 5a). It also corresponds to the end of the first monotonous increase of the friction coefficient. The second regime includes the steady increase of friction until reaching the plateau, and is a transition stage. During the transition regime, the standard deviation of friction increases, peaks, and decreases again. This observation indicates that the variability of the surface state on the disc is larger during this regime. The last regime, called the mature interface regime, is reached when the standard deviation of the friction coefficient during a lap definitively drops below 0.05 (Figure 5a), underlining a homogenization of the friction between the pin and the disc and thus, a homogenization of their surface state (see Discussion).

The influence of the track radius on the sliding distance needed to enter into the transition and mature interface regime is plotted in Figures 5c and 5d, for five tests of different track radii: MT024 ($R_{track}$ = 6 cm), MT029 ($R_{track}$ = 7.5 cm), MT030 ($R_{track}$ = 10 cm), MT037 ($R_{track}$ = 12 cm) and MT038 test ($R_{track}$ = 13 cm). The smaller the radius, the sooner the asperity-fault system enters in the transition regime and then in the mature interface regime (MT038 test never enters the mature interface regime). The duration of the transition regime (expressed in sliding distance) also increases with the track radius. This trend is non-linear.

The wear rate (expressed in µm/m), plotted for the MT024 test in Figure 5b, is computed as the average wear increment in a lap divided by the lap length $L_{track}$. The influence of the sliding regime and of the track radius on the wear rate is plotted in Figure 5d, with an error bar corresponding to the standard deviation of the wear rate during the regime. We observe that, for a given track radius, the wear rate systematically increases when going from one
<figure><img src="image_9.png" /><figcaption>**Figure 6.** Continuous and interrupted tests MT021 and MT022. (a) Comparison of the lap-averaged friction coefficient (in blue, on the left axis) and of cumulated wear (in red, on the right axis) between continuous (MT021) and interrupted (MT022) tests for 25 m sliding distance. The dotted line A (resp. the dotted line B) highlights the end of the run-in regime for the MT021 test (resp. MT022); (b) Evolution of apparent contact area and apparent contact stress for the interrupted test MT022.</figcaption></figure>

interface regime to the next. For example, in the case of the MT024 test, where $R_{track}$ = 6 cm, it is close to 30 µm/m during the run-in regime, 133 µm/m during the transition regime, and 226 µm/m during the mature interface regime. However, the wear rate for a given regime clearly tends to decrease when increasing the track radius. For example, for the run-in regime, for a radius of 7.5 cm, the wear rate is lower than 30 µm/m whereas for a radius of 12 cm, the wear rate decreases to 3 µm/m. The gap between the wear rates of the different regimes decreases with the radius. The same non-linear trend already noticed for the gap between the starting distance for the different regimes in Figure 5c can be guessed in Figure 5d. In a way similar to the friction coefficient, the wear rate variability is generally smaller for the mature regimes than for the run-in regime in Figure 5d.

## 3.2. Interrupted Test

In order to obtain an evolutive view of the interface processes, we conducted interrupted tests (MT020 and MT022). Both tests were replicates of two other continuous tests (MT018 and MT021 respectively), except that the sliding motion was stopped every meter, the contact was opened, and the pin surface topography was measured by interferometry. After the topography scan executed, the pin was replaced at the same location on the disc, with the same orientation, with a maximum error estimated at a few degrees of possible misorientation. In Figure 6a, the comparison between MT021 (continuous sliding) and MT022 (interrupted sliding) shows interesting differences between both cases. With a sliding distance of 25 m and a medium radius track ($R_{track}$ = 8 cm), the MT021 test just enters in the transition regime while the MT022 is not far from reaching the high value plateau of friction which is characteristic of the end of this regime. The difference in kinetics between the two tests is highlighted by the two vertical lines A and B in Figure 6a, which correspond to the end of the monotonous evolution of the averaged friction coefficient (i.e., run-in regime). The difference between the tests is certainly a consequence of the multiple operations of contact opening, pin dismounting, and topography measurement. These operations slightly disturb the interface, and appear to accelerate the kinetics of its evolution. In the early stages (first 5 m), the lap-averaged friction of the interrupted test is slightly larger, and increases at a faster rate than that of the continuous test. More interestingly, its increase is less regular which may also be a consequence of the manipulations every meter. At that stage, however, this does not have any effect on the wear rate, which is identical in both cases. For a sliding distance of ~6.5 m, when the averaged friction reaches ~0.2, the interrupted test shows a change of behavior, with larger friction fluctuations and an acceleration of the wear kinetics. At 9 m of sliding the wear rate considerably increases and so does the friction coefficient, albeit with an important delay (around 16 m of sliding). In contrast, the continuous test shows a very regular increase of the friction coefficient during the first 13 m of sliding, accompanied by a very low wear rate. The interface then progressively evolves toward the transition regime, with friction fluctuations and a progressive increase of the wear rate. It therefore appears that the repeated opening of the asperity interface associated with the interrupted test accelerates the evolution of this interface by a factor of ~2. In both cases, however, we observe the same evolution trends for the
<figure><img src="image_10.png" /><figcaption>**Figure 7.** Evolution of the topography of the pin during the interrupted test MT022 (25 m sliding test). All images are plotted with the same scale, and the color scale indicates topography in a local frame centered on the peak elevation of each image. Numbers in white indicate the cumulated sliding distance. For each image, contact inlet is on the left-hand side and contact outlet is on the right-hand side.</figcaption></figure>

averaged friction coefficient and the wear rate. We also note that the acceleration of wear always precedes the increase in friction. Similar results are found for the MT018 and MT020 tests (Figure S3 in Supporting Information S1). This offset underlines the fact that the products of wear (roughness and gouge) have consequences in the variations of the friction coefficient. We can assume, however, that the main physics are the same between the continuous and interrupted tests, albeit with different kinetics.

Figure 6b provides an estimate of the evolution of the apparent contact area, which can be estimated either from the Eddy-current sensor (assuming that most of the shortening of the contact originates from pin wear), or from the topographic measurements made during test interruptions. We checked that pin wear estimated by both methods are identical within measurement error (Figure S4 in Supporting Information S1). Results indicate that this area evolves from ~0.2 to ~30 mm² on the test duration. This leads to a dramatic decrease of the apparent normal stress in the contact, from ~400 to ~3.5 MPa (Figure 6b).

### 3.3. Surfaces Characterization

Figure 7 presents the pin's contact surface evolution, every meter of the MT022 test, with the contact inlet always oriented on the left-hand side. The first image is taken before the beginning of the test and shows the perfect half sphere of the pin, with a low (less than 1 µm) roughness level. The run-in regime, corresponding to the first seven images (sliding distance of the beginning of the transition regime is ~6 m), is characterized by moderate flattening of the contact's surface. At those stages, we observe the presence of a very smooth topographic plateau on each image, which certainly bears most of the normal load. This plateau occupies most of the apparent contact area in the image up to 4–5 m, but a more and more limited portion in the following maps. This correlates well with the fact that a transition in the wear regime just occurred at that point of the test (Figure 6a). From the 10 m map, the scanned surface area starts to increase at each measurement, which correlates with the acceleration in the wear
<figure><img src="image_11.png" /><figcaption>**Figure 8.** Differences between a high friction zone and a low friction zone during the transition regime of the test MT021 after 25 m of sliding. (a) Variations of the friction coefficient and the wear increment during the last lap; (b) Surface roughness of the high friction zone; (c) Surface topography of the high friction zone; (d) Surface roughness of the low friction zone; (e) Surface topography of the low friction zone; (f) Close view of the experimental pin showing gouge accumulation at the contact inlet (ellipse) and on the sides of the track (rectangles). Markers "g" indicate piles of loose powdery gouge.</figcaption></figure>

rate presented in Figure 6a. The surface is now well-abraded, and starts to show an important level of roughness. The smooth topographic plateaus made of agglomerated wear particles now appear and disappear during the transition period, and are smaller and rougher than in the early stages of the test. Finally, when approaching the mature regime (24–25 m scans), the contact surface has a homogeneous roughness and starts to develop different topographic features at the inlet and the outlet of the asperity: the inlet keeps the regular circular shape of the edge of the contact area, but the outlet is much rougher, less regular, and apparently fractured. The main hypothesis to explain the more intensive and damaging wear at the back of the contact surface comes from the shear stresses during sliding. At the contact inlet, the stress state is essentially compressive whereas at the outlet it is tensile because of friction forces. As rocks have a better capacity to bear compressive forces than extensive ones, we can assume that the contact outlet gets fragmented faster.

Same imaging techniques can be used for the post-mortem track. In Figure 8a, the last lap friction coefficient and the last lap wear increment of the MT021 test are plotted as functions of the angular position on the disc (25 m of sliding, early transitional regime, Figure 6a). High and low friction zones are identified and the topography of the wear track on the disc at these specific locations is acquired (Figures 8b and 8c). RMS roughness maps are provided for the same areas (Figures 8d and 8e). They are computed by first detrending the topography from its large-scale variations (using a gaussian filter with a sigma-value of 20 µm), and subtracting this moving average to the initial topography. A quadratic average of the residual topography is computed in each point using the same filter. In other words, the larger the RMS roughness in an area, the more this area presents large variations of height in the high spatial frequency domain. The high friction zone on the track spotted during the last lap of the MT021 (Figure 8a) presents a complex topography with holes and bumps (Figure 8b), and a typical RMS
<figure><img src="image_12.png" /><figcaption>**Figure 9.** SEM images of a pin in the transition regime (test MT021, 25 m of sliding). (a) Overview of the contact surface of the pin with the interferometer; (b) Overview of the contact surface of the pin with the SEM; (c) Zoom on a smooth plateau; (d) Zoom on the formation of the plateau, sintered third body particles; (e) Zoom on the powdered part at the back of the contact surface; (f) Zoom on a plateau with cracks.</figcaption></figure>

roughness of 3–6 µm. It is also characterized by big piles of loose gouge deposited on both sides of the track at each pass of the pin (Figure 8f). On the contrary, the low friction track area is hardly distinguishable from the intact disc surface (Figures 8c and 8e). The RMS roughness is close to 1 µm both in and out of the track. Only the regular depositions of granular gouge outside the track and the small parallel grooves on the topography map allow to guess where the track is. Thus, the main difference between areas exhibiting high friction and areas with low friction is the surface state of the tracks. Areas with high friction coefficient are rough, with holes and important gouge production and deposition. Some correlations can be done with the last lap wear increment. There is a trend linking the wear and the friction coefficient: when the local friction coefficient is higher, the local roughness is higher and this may lead to a higher wear in this area (around position 190° and 230° in Figure 8a, e.g.). It is not always the case (e.g., in the high friction zone) which underlines that the wear is not perfectly correlated to the instantaneous friction coefficient.

*Post mortem* contact surfaces of a pin in the transition regime (Figure 9) and a pin in the mature regime (Figure 10) are compared. In both figures, SEM images of the post mortem surface are shown along with zoomed views on the regions of interest. The contact inlet is oriented on the left-hand side. The contact surface of the pin of the MT021 exhibits the features of the transition regime (Figure 9b). A wide smooth plateau with an elongated shape, formed by the accretion of granular gouge particles, is present on a side of the pin (Figures 9c and 9d). Some other plateaus are visible, and some of them have some cracks oriented in the direction perpendicular to sliding (Figure 9e). At the contact outlet, a large proportion of the surface is covered by granular gouge (Figure 9f), with micrometric grain sizes. Some particles can also be found elsewhere on the contact surface (Figure 9e) but in smaller proportions.

A comparison with Figure 10 first confirms that the main difference between the post mortem contact surface of the MT021 test pin and the MT024 test pin is their size. The pin surface in the transition regime measures ~4600 µm of diameter against ~9670 µm for the pin in the mature regime, which has undergone higher abrasion. The contact surface of the MT024 pin is covered of granular powder (Figures 10d and 10e) of similar particle size
<figure><img src="image_13.png" /><figcaption>**Figure 10.** SEM images of a pin in the mature regime (test MT024, 34 m of sliding). (a) Overview of the contact surface of the pin from the interferometer; (b) Overview of the contact surface of the pin with the SEM; (c) Zoom on an intact rock patch; (d–e) Zooms on powdered regions.</figcaption></figure>

as on the MT021 pin. Several areas show bare rock surface (Figure 10c, and cross-section provided in Figure S5 in Supporting Information S1). In the mature regime, the coupled roughness of the pin (Figure 10a) and of the track (Figures 8b and 8d) explain the large wear rate during this regime (Figure 5d) and the large production of granular gouge (Figures 10d and 10e). In Figures 10d and 10e, one can also notice the successive layers of granular material overlapping, like a front of deposition progressing through the contact interface. These apparent plateaus are however very different from those of the transition regime (Figure 9), in the sense that the gouge is much less compacted and remains essentially granular.

## 3.4. Gouge Characterization

The particle size of the granular gouge is measured through laser scattering, which uses the scattering and diffusion processes occurring when a laser beam hits a particle. The particles are forced to go through a fixed laser beam, each particle scatters the light with an angle which is a function of its size. The scattered light is collected and the resulting scattered image is analyzed using an appropriate optical mathematical model (the Mie theory). This characterization is performed several times, with an increasing air pressure driving the particles in front of the laser, and the results are provided in Figure 11. We observe that, under low driving pressure, the size distribution of the gouge is essentially bimodal, with a characteristic size at ~300 µm and another one at ~10 µm. However, as the driving pressure is increased from 0.1 bar to 4 bars, large and fragile granular clusters get separated and the particle size distribution becomes more and more unimodal, with a characteristic size of ~3–4 µm. It is likely that this particular size is a better descriptor of the produced gouge. Around this mode, the size distribution is very wide, with equivalent diameters ranging from ~400 nm to ~1 mm.

To characterize the distribution of gouge in the interface, we mapped the topography of a worn track (Test MT022, 25 m of sliding, transition regime) at four locations. For each map, a first acquisition was performed, the map was cleaned with a brush, and the same region was immediately mapped again. By subtracting the track
<figure><img src="image_14.png" /><figcaption>**Figure 11.** Particle Size Distribution of the wear particles in collected gouge. Different curves correspond to different levels of driving air pressure used during measurement.</figcaption></figure>

topography before and after cleaning, we obtain a measure of the spatial distribution of the incohesive gouge on the track. An example of such a map is provided in Figure 12a, and other maps can be found in Figures S6–S9 in Supporting Information S1. It shows that, in the transition regime, gouge is present in the wake of the asperity, but is not evenly distributed. Some areas are covered by a gouge thickness that can locally reach a few tens of µm, and some areas are devoid of any form of powdery covering. After identifying the track direction on each map (dark dotted lines in Figure 12a), we can extract average cross sections of the gouge thickness and of the track beneath it. These cross-sections are stacked over all four measurement sites in order to build an average profile, which is provided in Figure 12b. It indicates that the track average wear depth is ~8 µm, on a width of ~4 mm. A large spatial variability exists (Figures S6–S9 in Supporting Information S1), with regions where wear is larger than 50 µm, and other regions that remain largely unworn. Figure 12c indicates that the average gouge thickness is in the range 3–10 µm, with large local variations. One should note that this is only the thickness of incohesive gouge, as the brushing process may have left in place some more compacted and adhesive layers.

# 4. Discussion

## 4.1. Sliding Regimes

Our experimental results indicate that the interface is submitted to three regimes that can be identified from mechanical data (Figure 5), and provide enough information to describe them in details. The different processes at work during these regimes are described using SEM images in Figure 13. Under constant normal load and linear velocity, interface kinetics are primarily controlled by the track radius (Figure 5c): the larger the track radius, the slower the interface evolution. The first stage is the run-in regime. It is characterized by a low but steadily increasing friction (Figure 4a) and a low wear rate (Figure 5d), despite the large value of the normal stress (several hundreds of MPa, Figure 6b). During this regime, the track remains largely intact and keeps its initial low roughness. The pin is characterized by a smooth and flat plateau made of a small amount of compacted gouge, which occupies the totality of the contact area (Figure 7). This plateau localizes accommodation, acts as a solid lubricant (Figure 13d), and maintains low friction and wear during several meters of sliding. It is able to persist in that state because of (a) the elevated normal stress and (b) the absence of a large roughness on the track. Wear is not totally absent, however, and eventually leads to a slow broadening of the contact area and to a degradation of the track surface. This partly disrupts the compacted plateau, and marks the entrance into the transitional regime.

The main characteristic of this second stage is the heterogeneity of both the track and the pin. The pin surface is now characterized by regions of smooth and compacted gouge plateaus, which indicate elevated local contact stresses, and regions covered by granular gouge (Figure 9). These plateaus are not as persistent as in the run-in stage, and migrate to various locations on the interface over time (Figure 7). Wear increases (Figure 5b), leading to a progressive flattening of the asperity, to an increase of the apparent contact area, and to a decrease of the apparent contact stress (Figure 6b). During the transition stage, lap-averaged friction increases from ~0.1–0.2 to ~0.7, over the course of a few tens of meters of sliding. This is related to the evolution of the track from an intact, smooth and clean state (Figures 8c and 8e) to a worn, rough and gouge-covered state (Figures 8b and 8d). On a given lap, however, friction coefficient is very heterogeneous (Map of Figure 3b). This is attributed to the heterogeneity of the track state, which arises from the fact that the kinetics of evolution vary in space. Hence, over a given lap, the asperity encounters both quasi-intact areas with a low friction (Figures 8c and 8e) which allow the existence of compacted gouge plateaus, and worn areas with a high friction (Figures 8b and 8d) which prevent it. This leads to the cyclic process described in Figure 13. The abrasion and fracturing of bare rock (Figure 13a) and the contact inlet constantly feed the interface with powdery gouge (Figure 13b). When the asperity meets a smooth section of the track (Figure 12a), the gouge layer is not disturbed by any incoming track irregularity, and gouge can accumulate and compact in areas of local high normal stresses (Figure 13c). This eventually leads to a sintering, perhaps aided by a limited local temperature increase in these highly-loaded and shear-localized regions, and to the appearance of smooth plateaus (Figure 13d), thereby reducing friction. However, when the
<figure><img src="image_15.png" /><figcaption>**Figure 12.** Gouge distribution on the track in the transition regime. (a) Spatial distribution of gouge obtained by subtracting worn and cleaned surfaces of a portion of track (Test MT022, 25 m of sliding); (b) Cross-section of the initial surface and cleaned surfaces, obtained by stacking cross-sections collected at four measurement sites (Figures S6-S9 in Supporting Information S1); (c) Average and standard deviation of the gouge thickness obtained by the same method.</figcaption></figure>

asperity eventually meets a worn and rough region of the track, these plateaus are disturbed (Figure 13e). They disintegrate and release powdery gouge in the interface, thereby increasing local friction, and the cycle can restart. During this period of constant creation/destruction of sintered plateaus, the standard deviation of friction on a given lap is high. However, as track gets more worn and homogeneous, this variability decreases (Figure 5a), because sintered plateaus have less and less occasions to form. Eventually, the friction coefficient is homogeneously high on the whole track, and this marks the entrance into the mature regime.

During this last stage, the track surface is homogeneously rough and covered by powdery granular gouge, in a way similar to Figures 8b and 8d. The pin surface is shared between gouge-covered and fractured bare rock regions (Figure 10). Sintered plateaus are not encountered any more, and are replaced by topographical features which resemble steps (Figure 13f), with a general orientation facing the contact inlet. In these regions, grains seem more compacted and more fine-grained than in looser regions, but the sintering process does not take place. This might be related to a lower normal stress and a less pronounced shear localization, which precludes any ductility to happen at the grain scale. Or it could be related to the mechanical disturbances associated with the pervasive track roughness, which constantly sweeps the gouge out of the asperity and uncovers bare rock regions. This regime is also characterized by relatively high wear rates, possibly reaching several hundreds of µm per m of sliding. This wear rate (expressed as a height loss) has to be multiplied by the increasing apparent contact area, which yields a considerable wear volume during this regime. This occurs while the apparent contact stress is much lower than in
<figure><img src="image_16.png" /><figcaption>**Figure 13.** Scenarios of interface evolution for the three regimes. (a) Bare rock; (b) Powdery gouge; (c) Compacted gouge; (d) Smooth plateau; (e) Broken plateau; (f) Topographical steps; (g) A typical lap-averaged friction signal over the three regimes.</figcaption></figure>

the early stages (i.e., as low as a few MPa, Figure 6b), and while the gouge thickness in the asperity contact is at its highest. This counterintuitive result indicates that, in the present configuration, powdery gouge does not act as a protective layer (as it did in the run-in regime for example), but rather as a wear-increasing agent. This is in good accordance with results obtained in tribological numerical models of granular and agglomerated third-body damaging effects on sub-surfaces and their consequences on wear (Bouillanne et al., 2024). From thereon, the tribological response of the asperity does not seem to evolve any more, and a steady state has been reached. We can hypothesize that this state reflects a balance between entering and exiting fluxes of gouge at the contact inlet and outlet, and gouge creation during bare rock surfaces abrasion. This regime is probably closer to the state of asperities on real faults than the first two regimes, which inherit from the (somewhat arbitrary) initial state of the pin and track surfaces. It should be reminded, however, that this equilibrium state corresponds to a moderate sliding velocity (0.01 m/s) and normal stress (a few MPa), and might be strongly modified if larger, co-seismic velocities were tested.

## 4.2. Influence of Roughness and Gouge

In order to decipher the influence of contact area, roughness and gouge layers on the evolution of the friction and wear regimes in the asperity, we ran additional tests: Standard tests were performed based on the protocol
<figure><img src="image_17.png" /><figcaption>**Figure 14.** Lap-averaged Friction coefficient (in blue) and Cumulated Wear (in red) of additional tests with artificial modification of the interface; (a) Influence of a new pin and a new track; (b) Influence of surfaces cleaning and gouge removal; (c) Influence of an additional compacted layer of gouge. Cartoons in the lower part of the figure represent cross-sections of the artificially-modified interface (orthogonal to the sliding direction).</figcaption></figure>

described in Section 2.2 up to distances of ~50–60 m of sliding, in order to reach the frictional steady state (Tests MT029, MT030, and MT034). The interface conditions were then artificially modified, and sliding was resumed for distances of ~20–40 m (Tests MT031, MT032, MT033, and MT034S). The modifications brought to the sliding interfaces were the following ones (Figure 14):

1. For test MT031, we combined the worn track of test MT029 with an intact pin.

2. For test MT032, we combined the worn pin of test MT029 with an intact track.

3. For test MT033, we kept the worn pin and track of test MT030, but we first cleaned them with a brush in order to remove all the incohesive powdery gouge.

4. For test MT034S, we kept the worn pin and track of test MT034S, but we first spread a large amount of powdery gouge (collected from several other tests) on the track and statically compacted it under a moderate load, until forming a dense layer, with a thickness estimated to a few hundreds of µm.

The evolutions of the friction coefficient and the averaged wear of the tests MT029, MT030, and MT034 are given as first part of the graphs of Figure 14, and match the observations made previously in Section 3.1, with a frictional plateau close to 0.7. However, the modifications artificially brought in tests MT031, MT032, MT033, and MT034S have an immediate and important influence on the tribological response, before the tribosystem asymptotically returns to its steady state after a few tens of meters of sliding. In Figure 14a, we observe that using an intact pin on a worn track leads to an immediate and sharp increase of friction (to a value of ~0.85) and wear during the first meters of sliding. This case corresponds to a situation where a large smooth asperity meets a rough surface under a large contact stress. Conversely, using the worn pin of a new track leads to a very large decrease of the friction (to a value of ~0.12) and of wear. This case corresponds to a situation where a rough surface slides on a smooth one, and shows a response analogous to the tests on intact tribopairs we describe in Section 3.1. These results indicate that the concept of roughness is not sufficient if it is taken at the wrong scale. In both cases, the local roughness computed at the sub-millimetric scale is the same in the tribopair (~1–2 µm on the smooth body and ~10 µm on the rough one). However, the roughness taken at a centimetric scale (i.e., accounting for the spherical or planar shape of the pin, seen as one of many asperities in a seismic fault) is different, and in the present conditions it appears that this scale cannot be ignored: the asperity geometry exerts a first order influence on the tribological response. This contradicts the hypothesis of a friction coefficient primarily controlled by the true contact area, since the latter is expected to be the same in both cases (as theory states that it only depends on material yield parameters and normal load (Rabinowicz, 1951)). In the present case, the apparent contact area is a
more relevant metric. At a centimetric scale, the concepts of compressional and extensional jogs on the fault surface (proposed in (Sibson, 1986)), with respective crushing and implosion brecciation, seems appropriate. This confirms the classical finding that, in a pin-on-disc friction test, different tribological responses arise if materials are switched in the tribopair (Blau, 1992).

Figures 14b and 14c illustrate the role of gouge in the contact: if we completely remove it (Figure 14b) or artificially increase its presence in the asperity contact (Figure 14c), friction increases by ~0.1–0.2. It seems to indicate that the gouge thickness and texture in the asperity during the established regime is somewhat optimal for limiting friction. In the absence of gouge, two bare rough surfaces are in sliding contact and micro-asperities meet and collide, increasing the energy expense in the contact. The wear rate, however, is not considerably modified (Figure 14b). Conversely, in the presence of a too large amount of compacted gouge, the asperity needs to push its way through this layer, which also increases the energetical cost of sliding. An unexpected result is the fact that wear rate (i.e., slope of red curves in Figure 14c) and friction are durably increased in the presence of a large amount of gouge. The pin apparently loses more than 3 mm of thickness before the gouge layer is completely consumed and the tribosystem returns to its steady state. This indicates a surprising persistence of the gouge layer along multiple passes of the asperity, while the latter continues to wear off at a high rate. Hence, the common view that the third body acts as a protective layer (Suggested in (Brodsky et al., 2011), and in (Fillot et al., 2005; Milanese et al., 2019; Mollon et al., 2023)) is challenged in the present conditions. The cumulated wear provided by our monitoring system corresponds to the loss of thickness of the entire interface. It therefore includes the effect of several phenomena (wear of the pin, wear of the track, changes in gouge thickness), and cannot properly discriminate between them. Based on the quantities provided in Figure 14 (several millimeters of cumulated wear) and on our observations, most of the measured wear is associated with pin shortening, but this would benefit from a more comprehensive monitoring of the interface state.

### 4.3. Friction and Wear in Carbonate Faults

Major earthquakes often take place in carbonate fault zones, and an important literature is devoted to lab-testing of friction and wear of this class of rocks. Depending on the experimental conditions, various values of the coefficient of friction were reported, from Byerlee-like high values of ~0.6–0.8 to very low values of ~0.1. This range is similar to our experimental results. Low friction was first attributed to the thermal decomposition of carbonates due to frictional heating (Han et al., 2010). The permeability of the resulting fault structure was found too low to confine the produced CO₂ and trigger fault pressurization. This led to the conclusion that the interface was probably lubricated by rolling calcite nanograins, which were described as submicrometric aggregates of 5–20 nm cristallites (Verberne et al., 2014; Siman-Tov et al., 2015). This class of smooth interface is generally called “Fault Mirrors” (FM) in the literature. This behavior is enhanced at elevated normal stresses and sliding velocities (Boneh et al., 2013), where nanograins are found to endure sintering, and similar tribological responses were also observed in fault rocks collected in the field (Tesei et al., 2014). It was later understood that FM did not require coseismic sliding rates to form (Verberne et al., 2014), and appeared without any thermal decomposition of calcite (Siman-Tov et al., 2015). Rather, they were found to form due to mechanical milling up to a grain size small enough to favor ductile deformation and “cold” sintering, and could therefore be destructed by brittle wear under less favorable conditions. It was later observed that this frictional regime led to a quasi-absence of wear (Boneh et al., 2013; Siman-Tov et al., 2015). The run-in regime described in our experiments corresponds well to these observations, as it occurs under a normal stress of several tens to hundreds of MPa and shows a very limited wear rate. A full scenario of formation of such surfaces in calcite gouge (involving strain localization in the granular gouge, development of patches of micro-slip surfaces, and coalescence in a unique fault plane in conjunction with recrystallization of the surrounding gouge) was later provided in (Smith et al., 2015; Pozzi et al., 2018). In this later reference, FM were proposed to be rheological boundaries of the actual Principal Slip Zone rather than the site of slip accommodation. FM were also observed after short coseismic sliding events under realistic crustal confining stresses in (Aubry et al., 2020), in conjunction with other surface aspects, for example, granular and scaly fabrics. The presence of fault mirrors was found to accelerate dynamic weakening (Smith et al., 2015) and to produce frictional healing rates one order of magnitude lower than those of other carbonate fault rocks, leading to a likely velocity-strengthening response (Park et al., 2021). Deciphering the way they form and disappear could be pivotal in the understanding of carbonate fault stability along seismic cycles.

The smooth load-bearing plateaus that we described in the run-in and transitional regimes of our experiments can certainly be described as fault mirrors. Many properties described in the literature are confirmed by our results: we
find that this tribological response is characterized by a limited wear rate and favored by elevated stresses (Boneh et al., 2013), and does not require large sliding velocities or important temperature elevations (Verberne et al., 2014). An interesting point is that the usual scenario for the formation of these structures involves a sufficiently thick gouge layer so as to allow localization, comminution and eventually sintering. While this scenario could be questioned in the presence of a single asperity system, our results show that fault Mirrors can also form under these conditions, including in cases where fault gouge is very scarce (our run-in regime). This requires however a sufficiently high normal stress and sufficiently smooth rock walls. Indeed, when normal stress decreases, plateaus are found to have a more and more intermittent life, and eventually disappear from the tribo-system. Surface roughening (also documented in (Aubry et al., 2020)) leads to a transition toward a more brittle and cataclastic wear regime: the typical grain size that we measured in the fault gouge produced during our mature regime was ~3 µm, which is much larger than the nanometric grains that were found necessary for fault mirrors. We may hypothesize that, in the presence of a single asperity with limited normal stress (a few MPa) and sliding velocity (0.01 m/s), the gouge layer is not sufficiently thick and sufficiently protected from the rock walls roughness to allow the comminution process. Most likely, the time of residence of gouge in the contact is also too low. Under these operating conditions, the kinetics of the scenario described in (Smith et al., 2015; Pozzi et al., 2018) are too slow and the fault mirrors are destroyed by brittle wear before being created, as shown in the cross-section of Figure S5 in Supporting Information S1. Instead, we observed a relatively coarse granular gouge with slip-perpendicular steps (similar to the scaly fabric described in (Aubry et al., 2020)) that might indicate unsuccessful attempts at slip localization. We may wonder if fault mirrors would develop in our single-asperity configuration in the mature regime if normal stress and/or sliding velocity were increased, since literature shows that this would accelerate their kinetics of formation. This will be the topic of future work in the lab.

### 4.4. Applicability to Natural Fault Conditions

The analogy between our experiments are real faults has clear limits that must be acknowledged. In the range explored in the present work, several operational parameters of the experiment are not completely in line with natural coseismic conditions. The normal stress in the asperity, although relevant to seismogenic depths in the early stages of sliding (several hundreds of MPa), quickly diminishes as the asperity flattens, and typically drops below 100 MPa after 5 m of sliding (Figure 6b). In the same line of reasoning, sliding distances of several tens of meters, as we investigate in this study, do not represent typical events, and our sliding velocity (0.01 m/s) is in the lower range of coseismic conditions. It is likely that, in order to explore friction and wear physics in a closer dialog with field data, future experiments will have to consider shorter and faster events, with a worn and gouge-covered track on the disc and a barely worn pin, in order to keep the contact pressure sufficiently high during the whole run while immediately submitting the asperity to a mature fault interface. This seems to be within the capabilities of our apparatus. Renewing (or not) the pin between successive runs will allow to investigate fault recycling along seismic cycles, while slide-hold-slide tests in dry and wet conditions and with various interface configurations will allow to constrain healing rates and enrich existing state-based friction laws.

## 5. Conclusion

We conducted single-asperity friction and wear tests on Carrara marble using a pin-on-disc apparatus inspired by the tribological practice. Our findings can be summarized as follows:

1. Despite the open character of this contact (as opposed to more closed contacts in triaxial or rotary shear experiments), fault gouge is generated and plays an important role in the tribological response of the contact. It is partly pushed away by the incoming asperity, but a certain amount of it is always present in the interface. It confirms that a complete understanding of the frictional response of geometrically complex faults must account for both aspects: geometrical asperities, and gouge rheology.

2. In the case of marble, a complex interplay develops between gouge and asperities. Under the conditions of our experiments, three regimes are systematically observed. In the run-in regime, the track and the asperity are largely intact, the contact is lubricated by sintered plateaus, and the friction and wear remain low. It is followed by a transitional regime where the track starts to wear off, but in a heterogeneous way, leading to a larger wear rate and to a progressive increase of the friction, with highly heterogeneous values depending on the surface met by the asperity. When the track eventually homogenizes, a steady state of high friction and wear is reached in all experiments. This occurs faster when the track radius is low, that is, when the frequency of asperity pass at each location of the track is higher. However, if any local property of the interface is modified (geometry of
the pin, roughness of the track, removal or addition of gouge), this steady state is disturbed during several
meters before being restored.

3. Calcite gouge controls local shear stress, thanks to its ability to form (or not to form) fault mirrors with low and stable friction and wear. However, such a layer can only be formed with certain kinetics under certain circumstances, such as high normal stress, high sliding velocity, and low roughness of the rock walls. It can also be destroyed by brittle wear if these conditions are not respected, and has an intermittent life. We can expect that, in a natural fault, local conditions under a given asperity are constantly evolving, depending on the properties of the other side of the fault and on the varying sliding velocity during a given event. The asperity itself is constantly being modified, for example, by flattening or roughening. Most likely, this leads to complex dynamics of permanent creation and destruction of fault mirrors under asperities. We can hypothesize that local friction under such an asperity (which represents most of the fault frictional force, since asperities are more highly loaded than the rest of the fault) therefore follows complex dynamics, which in turn interact with the dynamics of the sliding event. Whether or not a stable frictional response, with a firm weakening or strengthening character, may develop under such an asperity, will depend on the specific functional form of this dynamical system. Single-asperity friction and wear tests represent a promising candidate to explore and mathematize this dynamical system.

4. In a companion paper (Mollon et al., 2025), we propose a numerical model of a single fault asperity inspired by the experimental setup we describe in the present paper. This model is based on a coupled discrete/continuum framework, where both the pin and the track are allowed to damage and to release granular gouge, which can then evolve within the asperity interface, get ejected at the contact outlet, and eventually ingested again at the inlet thanks to periodic boundary conditions. While the complex material response of calcite gouge (comminution and fault mirror formation) is out of reach of this model, it nevertheless provides several predictions which are in good qualitative (and sometimes quantitative) agreement with our experimental results. Upon improvement and calibration on more experiments, it is expected to be a pivotal tool in the understanding of the local tribological response of fault asperities.

Data Availability Statement

The data generated is available at Mollon (2025).

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Acknowledgments

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