Earthquakes are natural phenomena resulting from abrupt accelerated sliding on tectonic faults. This sliding releases energy through seismic waves and heat (Niemeijer et al., 2012). Seismic waves propagate through the earth’s crust, causing surface vibrations, and earthquakes with significant magnitudes can result in substantial loss of life and property. Therefore, comprehending earthquake formation processes and mechanisms has become a relentless pursuit for numerous scientific researchers (Scholz, 1989; He et al., 1998; Marone, 1998; Mair et al., 2002; West et al., 2005; BenDavid et al., 2010; Kaproth and Marone, 2013). Brace and Byerlee (1966) introduced one crucial understanding of earthquake mechanisms, who suggested that the stick-slip phenomenon observed during the relative sliding of two rocks in laboratory experiments might be a mechanism for shallow earthquakes.

Since then, extensive laboratory friction experiments have been conducted to investigate the sliding properties of rock-rock interfaces (Johnson and Scholz, 1976; Scholz and Engelder, 1976; Engelder, 1978; Dieterich, 1979; Lockner and Okubo, 1983; Weeks and Tullis, 1985; Tullis, 1988; Kato et al., 1992; Karner and Marone, 2000). Nevertheless, lab-scale friction tests and seismic observations revealed that fault gauges in geological faults may play a critical role in earthquake initiation. These fault gauges consist of particles accumulated through surface wear over thousands of years due to friction.

The properties of fault gauges have a decisive influence on both the frictional strength and sliding stability of faults (Brace and Byerlee, 1966; Johnson et al., 1973; Sammis and Biegel, 1989; Frye and Marone, 2002; Mair et al., 2002; Anthony and Marone, 2005; Marone et al., 2008; Ikari et al., 2015; Scuderi et al., 2015; Jiang et al., 2016; Lieou et al., 2017; Hedayat et al., 2018). However, acquiring natural deep fault gauges without compromising their micromorphs and loading history is nearly impossible. To study the sliding properties of fault gauges, some scholars have used fault gauge samples collected from outcrops of fault surfaces (He et al., 2007). Various granular materials have also been used as simulants for fault gauges, assembled into the sliding surface of simulated faults in laboratories. These include pulverized particles obtained by manually grinding various rocks (Byerlee, 1978; Engelder, 1978; Morrow and Byerlee, 1989; Moore et al., 1997; He et al., 2007; Togo et al., 2011; Lu and He, 2014), industrially produced granular materials like finely ground glass beads (Géminard et al., 1999; Albert et al., 2001; Adjemian and Evesque, 2004; Härtl and Ooi, 2008; Johnson et al., 2013; Lastakowski et al., 2015; Rivière et al., 2018), MgO nanoparticles (Han et al., 2011; Yao et al., 2016), and even kitchen flour (Shinbrot et al., 2012; Leeman et al., 2015).

Within the framework of the rate- and state-dependent friction criterion, velocity weakening is a necessary condition for earthquakes to occur, while velocity strengthening typically cannot cause earthquakes (Scholz, 1998). Recent studies have shown that on some naturally seismogenic faults, creep on the fault during the seismic gap is unevenly distributed across the fault (Freymueller et al., 2000; Chlieh et al., 2008). This means that while some areas inside the fault are self-locking and undergoing stress recovery to prepare for the next earthquake, others are slowly creeping. These observations suggest the simultaneous existence of speed enhancement and velocity weakening on the same fault. In laboratory settings, some scholars have explored the influence of material inhomogeneity on fault belts’ sliding properties (Buijze et al., 2021; Bedford et al., 2022). Consequently, investigating the friction stability of fault gauges with different attributes greatly aids related research on laboratory earthquakes. Prior studies have indicated that gypsum behaves as a speed-weakening material at room temperature (Buijze et al., 2021), meaning that (a-b) < 0. As such, (a-b) of gypsum is fitted through stick-slip experiments and cannot be obtained by steady-state tests of speed steps. Conversely, calcite and kaolinite are velocity-enhanced materials at room temperature (Buijze et al., 2021), signifying that (a-b) > 0. However, the friction properties of their mixtures have not been systematically reported to date. Given these reasons, it holds significant scientific importance to study the changes in friction stability parameters (a-b) throughvelocity steptests of gypsum fault gauges under low normal stress conditions and steady-state tests of speed steps of kaolinite/calcite mixture fault gauges with different proportions.

The experiment was conducted at the Structural Physics Laboratory of the Institute of Geology, China Earthquake Administration. Gypsum, calcite, and kaolinite were purchased from Aladdin Company. We controlled the particle size of the gypsum fault gauge to 100–150 μm and that of kaolinite and calcite to 75–100 μm through grinding and sieving. To enhance the rigidity of the entire system and promote stable fault sliding, we used steel blocks for the surrounding rock of the fault. The steel blocks on both sides measured 100 × 50 × 50 mm³, while the middle steel block measured 150 × 50 × 50 mm³. The thickness of the fault gauge was 1.5 mm. Figure 1A shows the specific sample loading mode. Initially, we placed the assembled samples on the horizontal biaxial press, which had a maximum single-axis load capacity of 150 t and could be driven by either displacement or load control. We first loaded pressure in the F_x direction to the predetermined pressure, which was 0.9 MPa for the gypsum fault gauge experiment and 3 MPa for the kaolinite/calcite mixture experiment. Once the F_x direction reached the predetermined pressure, we controlled the F_y direction using displacement and performed shear experiments at speeds of 0.2, 1, 5, and 25 μm/s, allowing approximately 0.5 mm of slip under each speed condition until the sliding reached a steady state.

After completing the experiment, we determined the values of the friction stability parameters (a-b) based on the rate-state friction constitutive relation. Rate- and state-dependent friction is described using τ and refers to the conditions under which materials either strengthen or weaken with an imposed velocity step (Dieterich, 1979; Ruina, 1983). The Dieterich-Ruina formulation allows us to calculate τ as follows: τ τ = σ   μ 0 + a l n v v 0 + b l n θ v 0 D c , where σ represents the effective normal stress, and μ 0 is the friction coefficient when the slip velocity (V) equals the reference velocity ( v 0 ). The direct effect term ( a l n v v 0 ) accounts for the initial increase in frictional strength, while the evolution term ( b l n θ v 0 D c ) accounts for the reduction in frictional strength with slip distance and time, where D c denotes the critical slip distance, and θ denotes the state variable. The parameters a and b are empirical, dimensionless quantities that govern these terms. The term a −   b represents the velocity dependence of the material under specific environmental conditions, such as stress, temperature, slip velocity, and fluid effects (Marone, 1998). When the sliding reached a steady state, a − b = ∆ μ s / ∆ Ln   V .

Figure 2A illustrates the stable sliding behavior of different kaolinite/calcite mixtures under various loading rates (0.2–25 μm/s). As the proportion of kaolinite mass increases, the overall mixed fault gauge’s frictional coefficient gradually decreases. The frictional coefficient exhibits sudden changes during the experimental loading rate switching process, where an increase in loading rate results in a sudden increase in the frictional coefficient (Figure 2B), and a decrease in loading rate leads to a sudden decrease in the friction coefficient (Figure 2C).

Previous studies suggested that gypsum exhibits stick-slip behavior under different normal stress conditions at room temperature (Buijze et al., 2021). However, using steel blocks as the surrounding rock and a low effective normal stress of 0.9 MPa in our experimental design is not conducive to stick-slip in the gypsum fault gauge. Therefore, we observe a more stable sliding behavior in the gypsum fault gauge. The accuracy of the gypsum fault gauge’s (a-b) obtained through the steady-statevelocity steptest is superior to the value obtained by fitting the stick-slip data (Dieterich, 1979; Ruina, 1983). Additionally, the friction coefficient exhibits sudden changes during the experimental loading rate switching process, where an increase in loading rate leads to a sudden decrease in the friction coefficient, while a decrease in loading rate causes a sudden increase.

Based on the data, we derived the variation curves of different fault gauge frictional coefficients with loading rate, as shown in Figure 3A. Using the formula a − b = ∆ μ s / ∆ Ln   V , we determined that the slope of the curve in Figure 3 (middle) represents the (a-b) value of the fault gauge. The slope of the gypsum fault gauge is less than 0, indicating velocity weakening under this loading condition, with (a-b) approximately −0.01. Compared with the (a-b) value of −0.0031 (deMeer and Spiers, 1997) obtained through fitting the gypsum fault gauge under similar particle size conditions, our results show stronger velocity weakening. In contrast, the slopes of the kaolinite/calcite mixture fault gauges are all positive, indicating speed enhancement characteristics. Furthermore, as the kaolinite content increases, the slope of the curve becomes larger, suggesting that the (a-b) value of the material increases with the proportion of kaolinite. Additionally, we calculated the mixed fault gauge’s (a-b) for different kaolinite content, as shown in Figure 3B. This allowed us to establish the relationship between the mixed fault gauge’s (a-b) and kaolinite content. Through this relationship, we can estimate the mixed fault gauge’s (a-b) for different kaolinite mass fractions, providing a basis for future experiments and numerical simulations.

By designing a well-designed steady-state velocity step test, we successfully determined the values of (a-b) for both the gypsum fault gauge and the fault gauge consisting of different components of the kaolinite/calcite mixture. For the gypsum fault gauges, the (a-b) values obtained through near steady-statevelocity steptests and those reported in previous studies under similar conditions were negative. However, the (a-b) values obtained in our tests were one order of magnitude lower than those reported in previous studies, indicating that the gypsum fault gauge in our experimental setup exhibits a stronger tendency toward velocity weakening. Our steady-state velocity step tests on the kaolinite/calcite mixture fault gauges revealed that all mixtures, regardless of their kaolinite contents, exhibited positive (a-b) values. Furthermore, we observed a proportional relationship between (a-b) and the kaolinite content. As a result, we established a functional relationship between the (a-b) values of the mixture fault gauge and the mass fraction of kaolinite.