Frictional Experiments on Granitic Faults: New Insights into Continental Earthquakes and Micromechanical Mechanisms

Abstract

Granitic faults within the crystalline upper-to-middle continental crust play a critical role in accommodating tectonic deformation and controlling earthquake nucleation. To better understand their frictional behavior, we review experimental studies conducted under both dry and hydrothermal conditions using velocity-stepping (VS), constant-velocity (CV), and slide-hold-slide (SHS) tests. These approaches allow the quantification of frictional strength, velocity dependence, and healing behavior across a range of conditions. Our synthesis highlights that the friction coefficient of granite gouges decreases with increasing temperature and pore fluid pressure, decreasing slip velocity, and increasing slip displacement. The velocity-weakening regime shifts to higher temperatures with increasing slip velocity or decreasing pore fluid pressure. Temperature, normal stress, pore fluid pressure, and slip velocity interact to modulate frictional stability. In particular, microstructural observations reveal that grain size reduction, pressure solution creep, and fluid-assisted chemical processes are key mechanisms governing transitions between velocity-weakening and velocity-strengthening regimes. These insights support the growing application of microphysical-based models, which integrate micromechanical processes and offer improved extrapolation from the laboratory to natural fault systems compared to classical rate-and-state friction laws. The collective evidence underscores the importance of considering fault rheology in a temperature- and fluid-sensitive context, with implications for interpreting seismic cycle behavior in continental regions.

1. Introduction

Earthquakes on crustal faults are dominated by granitoid gouges, which mostly range between depths of 2 and 18 km and provide information about the location and style of deformation of the fault in this upper-crustal “seismogenic” zone (e.g., the San Andreas Fault). With increasing temperature (depth), the frictional (brittle)–viscous (ductile) transition in these fault gouges plays a crucial role, as it represents a significant shift in the rheological behavior of the Earth’s lithosphere. This transition also aids in defining the lower limit of the seismogenic zone, which is the region where large-magnitude earthquakes typically initiate [1,2], such as the depth distribution of earthquakes in the central creeping section of the San Andreas Fault [3,4,5], the Kellyland Fault in eastern Maine [6], the Alpine Fault in New Zealand [7], and the Alps Fault [8], as well as the Anninghe–Xianshuihe Fault zone on the southeastern boundary of the Tibetan Plateau [9,10]. Understanding the depth distribution and sliding characteristics of seismogenic zones is crucial, as it not only delineates where large-magnitude earthquakes are likely to initiate but also provides insights into the diverse slip mechanisms that characterize fault zones. Nevertheless, the direct observation of fault mechanics at seismogenic depths remains technically challenging due to the extreme in situ conditions. In this context, laboratory friction experiments provide a valuable approach to simulate and systematically investigate the physical and chemical processes that control fault strength and stability under controlled temperature, pressure, pore fluid, and slip rate conditions that are representative of various depths within the continental crust.

Fault slip events can span a range of scales, from a few millimeters to several hundred kilometers, and occur over time scales ranging from fractions of a second to millions of years, which causes the distribution of slip thickness on field faults to range from ~1 mm to 1 cm [11,12]. A complex multi-mode slip is associated with various types of earthquake phenomena [13], including regular earthquakes [14], slow-slip events [15,16], low-frequency earthquakes [17,18], episodic tremor and slip [19], and aseismic creep [20,21]. In terms of crustal deformation, the loading cycle is often divided into four phases, preseismic, coseismic, postseismic, and interseismic, called the earthquake periods. The concept of the seismic cycle was first formalized by H.F. Reid [22], who proposed the elastic rebound theory based on his investigation of the 1906 San Francisco earthquake along the San Andreas Fault. According to this model, tectonic motion causes elastic strain to accumulate on faults locked by friction until failure occurs, and stored energy is suddenly released during an earthquake [23]. While this conceptual framework provides a first-order understanding of earthquake occurrence, the detailed physical processes governing strain accumulation, fault strength, and instability remain incompletely understood. Laboratory friction experiments offer a controlled means to investigate these processes by replicating the stress conditions, slip behaviors, and microstructural evolution of fault zones, thereby providing empirical constraints on the mechanics of the seismic cycle at different depths. Bowden and Tabor [24] developed the adhesion friction theory, which revolutionized the understanding of the frictional behavior of stick–slip instability at the microscopic level. Brace and Byerlee [25] inferred that the recurrence of stick–slip could be a possible mechanism for shallow-focus earthquakes. Moreover, studies on the preseismic period focus on the analysis of frictional weakening or strengthening before failure, the development of nucleation zones, and the study of slow-slip events [26,27,28]. Coseismic deformation is replicated by rapidly increasing the slip rate to simulate fault rupture, including the role of dynamic weakening, temperature changes, and the potential formation of a fluid film or molten material at the fault interface [29,30]. The processes of the postseismic period examine afterslip and time-dependent healing processes, such as fault restrengthening and viscoelastic effects [2], aftershock distributions [31], and the interaction between small repeated earthquakes [32,33]. Research in the interseismic period focuses on the rate-and-state friction (RSF) laws, which describe how friction evolves with time and the slip rate [26,34,35].

There are differences in shear strength between different shape types in rock and gouges [4]. Experiments have demonstrated the effects of temperature, sliding rate, pore fluid pressure, normal stress, and shear displacement, as well as microstructure, on friction properties and associated seismic behaviors [9,36,37,38,39,40,41]. Friction experiments have been conducted using different types of instruments, including the rotary shear apparatus [42,43]; saw-cut apparatus [44]; direct-shear apparatus [45]; and double-direct shear [28] (Figure 1). Within the RSF framework, two experimental approaches are particularly important in investigating frictional properties: (a) velocity stepping, which is ideal for investigating how friction varies with sliding velocity and understanding velocity dependence [46,47], and (b) slide-hold-slide, which focuses on the healing or strengthening of the fault interface during periods of inactivity [48,49].

The frictional behavior of granitoid material under dry and hydrothermal conditions has been extensively studied through laboratory experiments, limited in situ studies, and numerical modeling. However, there appears to be a lack of review articles focusing on frictional strength and slip stability in relation to continental earthquake nucleation and the latest friction models. Marone [27] reviewed the standard RSF model, highlighting frictional healing at room temperature and discussing earthquake afterslip in relation to laboratory data within this model framework. Hu and Sun [50] investigated the impact of temperature and pore fluid pressure on the nominal friction coefficient of rocks but did not consider the rate-and-state effects and frictional stability. Also, Mei et al. [51] emphasized the influence of temperature on hydrothermal conditions but did not consider the effects of pore fluids, slip rate, and healing mechanisms on the seismic cycle. In contrast to these reviews, the present study specifically addresses the temperature, rate, and pore fluid pressure dependence of frictional stability, focusing on the velocity dependence of rock friction and physically based friction models.

We first review the standard RSF laws, followed by an extensive review of the results from hydrothermal friction experiments on granitic gouges, emphasizing the steady-state friction (including healing) and frictional stability parameters. Next, we analyze the deformation mechanisms that influence frictional strength and slip stability and summarize physically based constitutive friction laws. Finally, we propose several open questions for future research and highlight the key conclusions.

Figure 1. The laboratory fault systems. The sketches of (a) the direct shear setup [48], (b) double-shear setup [28], (c) saw-cut setup [37], and (d) rotary shear setup used for the laboratory friction experiments. The frictional interface is assumed to be filled with granular gouges or simply a bare rock surface. (e) The simulated fault systems can be simplified into a spring–slider system. The slider is driven by a load point velocity of V_L and slides along a frictional interface at a slip velocity of V via a spring with stiffness K. The frictional resistance is τ. (f) A schematic drawing of the rate- and state-dependent friction parameter estimation during a change of load–point velocity from V₀ to V₁, Figure reproduced from [51] with permission.

Figure 1. The laboratory fault systems. The sketches of (a) the direct shear setup [48], (b) double-shear setup [28], (c) saw-cut setup [37], and (d) rotary shear setup used for the laboratory friction experiments. The frictional interface is assumed to be filled with granular gouges or simply a bare rock surface. (e) The simulated fault systems can be simplified into a spring–slider system. The slider is driven by a load point velocity of V_L and slides along a frictional interface at a slip velocity of V via a spring with stiffness K. The frictional resistance is τ. (f) A schematic drawing of the rate- and state-dependent friction parameter estimation during a change of load–point velocity from V₀ to V₁, Figure reproduced from [51] with permission.

2. Friction Motions and Friction Law

Through extensive experiments, Dieterich [26] and Ruina [35] demonstrated that rock friction is influenced by both sliding velocity (V), a state variable ($\theta$), and normal stress ($\sigma$). Dieterich interpreted D_c as representing the slip necessary to renew surface contacts; in that case, the ratio ${\displaystyle \frac{D_c}{V}}$ defines the average contact lifetime $\theta$. They proposed that the frictional shear stress $\tau$ could be described as

$$\tau =\overline{\sigma }\left[{\mu }_0+aln\left({\displaystyle \frac{V}{V_0}}\right)+bln\left({\displaystyle \frac{V_0\theta }{D_c}}\right)\right]$$

(1)

where $\overline{\sigma }$ is the effective normal stress equal to the difference between the total normal stress (${\sigma }_{\mathrm{n}}$) and pore fluid pressure ($P_{\mathrm{f}}$), and ${\mu }_0$ is the steady-state friction coefficient at a reference sliding velocity of $V_0$.

The meanings of the parameters a, b and D_c can be illustrated by an idealized velocity stepping test (Figure 1f) of a spring block system (Figure 1e). If the block is sliding at a steady velocity of V₀ and the velocity is suddenly increased to V₁ (a sudden change requires an infinitely stiff spring), the friction suddenly increases by aln(${\displaystyle \frac{V_1}{V_0}}$). The friction stress then decays by an amount bln(${\displaystyle \frac{V_1}{V_0}}$) roughly exponentially over a characteristic distance D_c. If (a − b) > 0, the new steady-state shear stress is greater than the old one, and the behavior is said to be “velocity strengthening”. If (a − b) < 0, the new steady-state shear stress is below the old one, and the behavior is “velocity weakening”.

The decay of the shear stress is governed by the evolution of the state variable $\theta$. This is described by either the aging law [26]

$${\displaystyle \frac{d\theta }{dt}}=1-{\displaystyle \frac{V\theta }{D_c}}$$

(2)

or the slip law (Ruina, 1983) [35]

$${\displaystyle \frac{d\theta }{dt}}=-{\displaystyle \frac{V\theta }{D_c}}\ln \left({\displaystyle \frac{V\theta }{D_c}}\right)$$

(3)

The main difference between the two descriptions is that for zero velocity, $\theta$ increases linearly with time for the aging law, but for the slip law, it changes only with non-zero velocity. Nevertheless, both laws give the same value for the steady state $\theta$ = 0, ${\theta }_{\mathrm{ss}}$= ${\displaystyle \frac{D_c}{V}}$ and linearize to the same expression. Notwithstanding this difference, the two evolution laws (2a) and (2b) also have several common features. First, under a steady state, the state variable is a constant given by ${\theta }_{ss}$= ${\displaystyle \frac{D_c}{V}}$ and in particular, ${\theta }_{*}$= ${\displaystyle \frac{D_c}{V_{*}}}$. Second, the steady-state frictional strength, Equation (1) becomes

$${\mu }_{ss}={\mu }_0+\left(a-b\right)ln\left({\displaystyle \frac{V_{ss}}{V_0}}\right),$$

(4)

and the behavior is “velocity weakening” or “velocity strengthening” depending on the sign of (a − b).

The spring block system is an adequate representation of experiments in which slip occurs roughly simultaneously over the frictional surface within the precision of measurements. However, for a slip in a continuum, as in the earth, the stiffness depends on the length of the slipping zone [52,53] and, in this case, the results of the spring block system are only an analog to earthquake behavior. While the classical RSF framework effectively describes fault slip behavior at low-to-intermediate velocities and over a broad range of geological conditions, it becomes increasingly limited at seismic slip rates (V > 1 m/s), especially under hydrothermal conditions. At such high velocities, additional dynamic weakening mechanisms must be considered to account for the dramatic reductions in friction observed in laboratory experiments and inferred from field observations [54,55]. However, the present review primarily focuses on experimental studies conducted under the slower slip rate (V < 1 mm/s) relevant to earthquake nucleation conditions.

3. Friction Experiments of Granitoid Fault

The standard RSF law, derived from laboratory friction experiments, has been extensively utilized to quantify the frictional properties of rock faults and simulate the various stages of both natural and induced seismic events [27,56,57,58], as well as laboratory earthquakes [37,59,60,61]. This includes the preseismic, nucleation, coseismic, and interseismic healing processes. The RSF framework effectively captures a broad spectrum of fault slip behaviors, ranging from stable sliding to slow-slip events and dynamic ruptures. In this section, we summarize laboratory friction experiments under both dry and hydrothermal conditions for diverse granites and their gouges (Table 1). Friction experiments were conducted using various apparatus, such as saw-cut, direct-shear, double-direct-shear, and rotary-shear configurations. These various experimental setups facilitated the investigation of frictional strength variations under constant-velocity slip, the assessment of velocity dependence parameters (a − b) during velocity-stepping tests, and the evaluation of fault healing behavior through slide-hold-slide experiments [26].

As a fundamental basement rock in the continental upper crust, granite and its fault gouges have been extensively investigated in laboratory experiments since the 1950s. We focused on the frictional properties of rocks/gouges under varying temperatures, normal stress, pore pressure, and sliding rate, which are key parameters controlling granite fault mechanical behavior. Given that in situ crustal conditions exhibit linear-like gradients in temperature and pressure with depth (geothermal gradient: 25−30 °C/km), understanding earthquake nucleation and induced seismic under coupled thermos-hydro-mechanical conditions remains a central scientific challenge. Early friction experiments were primarily conducted on Westerly granite, which is composed predominantly of ~28% quartz, ~35% plagioclase, ~34% K-feldspar, and <5% biotite [27,62] but with biotite replaced by chlorite and muscovite. Subsequent studies have incorporated natural fault gouges retrieved from continental drilling projects and fault cores, which are characterized by higher proportions of illite- and chlorite-rich components [7,9,40,41,63].

Table 1. Friction experiments on granitoid gouge/rock.

Gouge/Rock Sample	Temperature T (°C)	Effective Normal Stress $\overline{\mathit{\sigma }}$ (MPa)	Pore Fluid Pressure ${\mathit{P}}_{\mathit{f}}$ (MPa)	Slip Rate V (μm/s)	Shear Displacement S (mm)	Experiment Type	References
Westerly granite	ambient	2–10	dry	0.1–10	~1		[64]
Westerly granite	ambient	27–84	dry	0.01–10	~70	Bare surface, CV/VS	[65]
Westerly granite	ambient-845	CP: 250	dry	0.0476–0.476–4.76	~4	VS	[36]
Westerly granite	ambient	50	dry	0.001–3000	~376	VS	[66]
Westerly granite gouge	25–600	400	dry, 100	0.01–0.1–1	~4	VS	[37]
Westerly granite gouge	ambient	25	dry	1–10	~400	VS	[38]
Granitoid gouge	100–600	200	30	0.04–0.2–1	~4	VS	[67]
Granitoid gouge	100–600	100, 200, 300	30	0.04–0.2–1	~4	VS	[40]
Westerly granite, gouge	25–600	5–40	minor water	0.1–30	~2.5 or ~112	VS	[45]
Natural granite gouge	25–600	200	30	0.04–0.2–1	~4	VS	[68]
Westerly granite gouge	25–250	CP: 20	10	0.1	~5	HSH	[69]
Natural granitoid gouge	20–650	100	100	0.1–100	~15	CV	[41]
Natural granite gouge	25–600	100, 200	30,100	0.04–0.2–1 and 1–3-10–30-100	~25	VS and CV	[9]

Note. VS = velocity stepping, CV = constant velocity, SHS = slide-hold-slide, CP = confining pressure.

Table 1. Friction experiments on granitoid gouge/rock.

Gouge/Rock Sample	Temperature T (°C)	Effective Normal Stress $\overline{\mathit{\sigma }}$ (MPa)	Pore Fluid Pressure ${\mathit{P}}_{\mathit{f}}$ (MPa)	Slip Rate V (μm/s)	Shear Displacement S (mm)	Experiment Type	References
Westerly granite	ambient	2–10	dry	0.1–10	~1		[64]
Westerly granite	ambient	27–84	dry	0.01–10	~70	Bare surface, CV/VS	[65]
Westerly granite	ambient-845	CP: 250	dry	0.0476–0.476–4.76	~4	VS	[36]
Westerly granite	ambient	50	dry	0.001–3000	~376	VS	[66]
Westerly granite gouge	25–600	400	dry, 100	0.01–0.1–1	~4	VS	[37]
Westerly granite gouge	ambient	25	dry	1–10	~400	VS	[38]
Granitoid gouge	100–600	200	30	0.04–0.2–1	~4	VS	[67]
Granitoid gouge	100–600	100, 200, 300	30	0.04–0.2–1	~4	VS	[40]
Westerly granite, gouge	25–600	5–40	minor water	0.1–30	~2.5 or ~112	VS	[45]
Natural granite gouge	25–600	200	30	0.04–0.2–1	~4	VS	[68]
Westerly granite gouge	25–250	CP: 20	10	0.1	~5	HSH	[69]
Natural granitoid gouge	20–650	100	100	0.1–100	~15	CV	[41]
Natural granite gouge	25–600	100, 200	30,100	0.04–0.2–1 and 1–3-10–30-100	~25	VS and CV	[9]

Note. VS = velocity stepping, CV = constant velocity, SHS = slide-hold-slide, CP = confining pressure.

3.1. Velocity-Stepping Experiment

Velocity-stepping (VS) experiments are widely used in the study of fault friction properties. In VS friction experiments, variations in shear velocity are systematically applied to investigate the rate-dependence of frictional behavior in fault materials, which is critical for assessing slip stability in earthquake nucleation zones (e.g., the values of (a − b)). These experiments are typically conducted using high-stiffness shear apparatuses, most commonly direct-shear, saw-cut, and rotary shear configurations [64,70]. The direct-shear apparatus is mechanically straightforward and allows for easy sample assembly and force alignment (Figure 1a,d). It is well-suited for low-to-moderate slip rates (μm/s-mm/s) and small displacement (<10 mm) experiments, making it ideal for studying quasi-static frictional properties. Its primary advantages include the direct application of shear load and ease of data interpretation. However, its limitations include relatively small cumulative displacements and potential boundary effects, such as stress concentrations at the sample edges, which can affect the uniformity of deformation. In the saw-cut test, the servo-controlled triaxial machine is capable of independently controlling axial stress, confining pressure, and pore pressure. This setup allows the simulation of realistic in situ stress conditions relevant to crustal fault zones, particularly under elevated pressure and temperatures. However, the total shear displacement achievable is typically constrained (<4–5 mm). In contrast, the rotary shear apparatus employs torsional motion to impose shear displacement, allowing for continuous sliding at a wide range of velocities and large total displacements. This makes it particularly suitable for simulating seismic slip conditions and capturing thermomechanical processes during rapid fault motion. Despite these advantages, rotary systems are generally more complex, require careful alignment, and involve non-uniform stress distributions due to their radial geometry. Data interpretation also requires the conversion of torque and angular displacement into shear stress and slip, which adds to the analytical complexity. The choice of apparatus depends on the experimental objectives and the specific slip conditions of interest.

We summarized the VS test on granitic examples and discussed the mechanisms that influence their sliding stability. At dry conditions (P_f = 0 MPa), the velocity dependence of friction, that is, on (a − b) values only, shows the positive (V-S behavior) under all temperatures (T) and velocities (V) (Figure 2) [36]. However, V-W behavior can also be observed in the nominally dry tests, although such results should be interpreted with greater caution [45]. Beeler et al. [38] conducted friction experiments under room T at an effective normal stress (${\mathsf{\sigma }}_{\mathrm{n}}^{\mathrm{eff}}$) of 25 MPa, and granite fault gouges show the V-W behavior occurring up to ~40–100 mm displacement, then giving way to V-S behavior.

On the contrary, three T regimes were observed under hydrothermal conditions for granitic gouge and rock: (a) (Regime I) velocity-strengthening (V-S) at a low T of 25–100 °C; (b) (Regime II) velocity-weakening (V-W) at an intermediate T of 150–300 °C; (c) (Regime III) velocity-strengthening (V-S) at a high T of 350–600 °C. Notably, the boundaries of these T ranges may shift toward a higher T with different V and P_f. Blanpied et al. [37] found that at 350 °C, lower V (0.01–0.1 μm/s) transition from the V-W regime to a high-T, V-S regime earlier than higher V (0.1–1 μm/s). A similar trend is observed in the natural granite gouge [9]. They conducted friction experiments over a wider V range of 1–100 μm/s and found that the V-W regime occurs at 150–300 °C for low V = 1–3 μm/s, while it extends to 100–450 °C as the V increases to 30–100 μm/s (Figure 2). In addition to T and V, pore pressure (P_f) and shear displacement influence the occurrence of the three regimes. For example, increasing P_f shifts all three regimes toward lower T, particularly narrowing the V-W regime to within 100–350 °C. This behavior has also been observed in phyllosilicate and quartz-rich fault gouges [71]. Regarding shear displacement, large cumulative slips can promote an earlier transition from the V-W regime to a high-T, V-S regime [9]. Note that in tests conducted over a narrow range of V, the (a − b) values may capture only two of the three frictional regimes [40,68,72].

Recent microstructural studies suggest that the transitions among the three frictional regimes are primarily governed by underlying microphysical mechanisms, particularly the intergranular flow and deformation of fine-grained gouge facilitated by intergranular pressure solutions, often accompanied by healing processes, such as cavitation–creep behavior, and CNS models [42,72,73,74,75]. Under hydrothermal conditions, the strain rate of the fine grains is strongly dependent on temperature (T), differential stress ($\sigma$), and grain size (d). These relationships are commonly described by the flow laws of the diffusion creep

$$\dot{\epsilon }=A{\sigma }^n{d}^{-m}\exp \left({\displaystyle \frac{-Q}{RT}}\right)$$

(5)

where A is a constant value, n is the stress exponent, m is the grain size exponent, Q is the activation energy, R is the gas constant, and T is the absolute temperature. Accordingly, elevated temperature and differential stress, along with finer grain size, contribute to an increased strain rate [76,77]. The typical microstructural observations of dissolution reveal widespread intergranular indentation features and grain-to-grain contacts in granite gouges at T above 600 °C [9,41]. Pressure solutions in the field are commonly recognized by the development of stylolites, solution seams, and sutured grain boundaries. These structures are most frequently observed in sedimentary rocks, especially in carbonates and quartz-rich gouges, where mineral solubility and the presence of pore fluids promote the pressure solution process [78,79]. However, to quantitatively resolve the understanding of microphysical controls on the transition between stable and unstable sliding, more extensive frictional experiments on granite are required under a broader range of conditions, particularly at lower velocities and higher pore pressures.

3.2. Constant-Velocity Experiment

Constant-velocity friction experiments are fundamental for characterizing the steady-state friction strength of faults or the continental crust. These tests enable systematic observations of the shear stress–strain response, including peak strength, strain weakening, and steady sliding behavior. In recent decades, advances in experimental techniques have allowed for the simultaneous monitoring of porosity, volumetric strain, and acoustic emissions during shear. These additional datasets provide critical insights into the micromechanical processes, such as dilation, compaction, and grain-scale damage, that govern fault zone evolution during slip. Here, we mainly summarize the friction strength or coefficient changed by temperature (T), normal stress (${\sigma }_{\mathrm{n}}$), velocity (V), and pore pressure (P_f).

Under dry conditions, granitic and quartz–feldspar materials exhibit high friction coefficients (μ) typically ranging from 0.6 to 0.8 across both low- and high-temperature (T) regions, consistent with Byerlee’s law. For example, Lockner et al. (1986) [36] showed a high μ, which increased slightly over a T range of ~20–800 °C (normal stress ranged from 380 to 460 MPa). Also, in a study by Stesky [80], dry westerly granite exhibited relatively high μ at 300–700 °C (normal stress ranged from 370 to 450 MPa). Tullis and Weeks [65] conducted a shear test on dry granite rock with a bare rock surface at V = 0.01–10 μm/s, further confirming high μ. The experimental results on natural granite gouges indicate that at T = 600 °C and an effective normal stress (${\sigma }_{\mathrm{n}}^{\mathrm{eff}}$) of 100 MPa, the μ in dry conditions remains at a value of 0.68 [9]. Compared to dry fault gouges, wet granite gouges exhibit a broader range of friction coefficients. At Ts below 400 °C, there is no difference between dry and wet conditions; however, above 400 °C, the μ decreases significantly with increasing pore pressure (P_f). In particular, at 600 °C and a low velocity (V) of <1 μm/s, the μ values can decrease to ~0.4 [9,37]. In addition to T, P_f, and V, the shear under large displacement also changed the μ at 600–650 °C. The μ decreases from 0.75 to 0.39 with increasing shear displacement from 4 to ~20 mm [9,41] (Figure 3).

The microstructural evidence indicates that high μ (>0.6) corresponds to a temperature-insensitive regime, which is dominated by frictional deformation, while low μ (<0.6) corresponds to a temperature-sensitive regime, which is mainly governed by frictional deformation, potentially accompanied by plastic deformation [81]. In high μ, the deformed granite gouge shows a cataclastic frictional granular flow, and the angular grain boundaries suggest a process of grain crushing and fracturing in the slip zone. In that case, high strength is mainly determined by the actively deformed slip zones, where frictional resistance is caused by grain rotations and localized sliding along angular grains and on the fracture array. However, at lower μ, microstructural observations reveal evidence of localized shear bands, including Riedel shear, Boundary shear, and Y-shear [82], accompanied by intergranular pressure solution and granular flow. In particular, shear localization in granular materials plays a critical role in controlling both their frictional strength and deformation characteristics. In this regime, the extremely fine-grained gouge exhibited few fracture arrays, and many nanopores were located along the grain contact surfaces, and these features are commonly observed in naturally deformed rocks from mid-crustal shear zones [83,84,85]. These nanopores likely involve a combination of processes of intergranular sliding and dissolution–precipitation creep (DPC), and they infer that such low friction strength caused by the finer-grain size within the principal slip zones allows DPC to operate at rates that are sufficiently rapid to accommodate most of the sliding and ultimately resulting in a reduction in the gouge strength [9,41,42].

3.3. Slide-Hold-Slide Experiment

Laboratory slide-hold-slide (SHS) experiments serve as a fundamental analog for studying the seismic cycle and are widely employed to measure strength recovery in simulated fault systems. SHS tests consist of alternating periods of induced stick–slip and quasi-static holds during which time-dependent strength recovery occurs. The strength changes according to secant friction $\mu =\tau /\left({\sigma }_{\mathrm{n}}-P_{\mathrm{f}}\right)$, $\tau$ and ${\sigma }_n$ are shear and normal stress measured on the fault surface, and $P_{\mathrm{f}}$ is pore pressure. The magnitude of restrengthening ($\Delta \mathit{\mu }$) is calculated by the difference between the peak failure strength upon the resumption of the slip and the steady-state sliding strength preceding the hold (Figure 4). With subsequent shearing, the shear stress gradually declines to its original steady-state value (${\tau }_{\mathrm{ss}}$). Seismic observations reveal that the drop in earthquake stress rises logarithmically over time, while studies on rock friction demonstrate that restrengthening increases with the log of hold time, an equation that can be characterized by the logarithmic relation defined in previous studies [49,64,86].

Previous studies under room temperature (T) indicate that the frictional healing rate is sensitive to time and the slip rate. Marone [27] conducted an SHS test under constant normal stress of 25 MPa using quartz sand sheared between rough westerly granite surfaces. The results indicate that the friction decreased during hold periods, reaching a peak value (the steady-state friction coefficient) when reloaded. Additionally, friction increased almost linearly and logarithmically with the hold time. This trend is consistent with many other earth materials [87,88,89,90]. However, when the T increases to levels corresponding to the shallow crust, the friction coefficient of westerly granite linearly increases with T, but T has little effect on the rate of change in static friction with hold time. It is cautioned that extrapolating laboratory results to natural faults should be undertaken carefully. Neglecting the effect of T could lead to an underestimation of the fault strength under dry conditions by up to 10% [45]. Recent studies show that frictional weakening was observed in hydrothermal SHS tests at Ts ≥ 200 °C, indicating that SHS tests are more effective in promoting weakening than VS tests [37]. The simulation of long-duration holds at 250 °C further suggests that hydrothermal alterations occur at this T because the negative state variable is not required to simulate shorter hold periods or lower Ts. Although the precise mechanisms controlling frictional behavior remain unclear, the data imply that the processes involved are water-assisted, temperature-dependent, and chemically complex with a characteristic time delay in the order of 1000 s [69]. Jeppson et al. [91] measured the restrengthening of wet quartzite samples under a broader range of effective normal stress of 20–200 MPa. The restrengthening ($\Delta \mathit{\mu }$) increases with the log of hold duration, the 200 °C healing rate, and the 0.014 per e-fold increase in time, which is comparable to that determined from seismological observations along the Calaveras Fault. Overall, they indicate that cohesive healing is negligible at Ts < 200 °C, and strength recovery is predominantly due to frictional healing processes.

Figure 4. (a) Schematic diagram of restrengthening or secant friction evolution during slide-hold-slide (SHS) tests. (b) Diagram showing how secant friction (blue lines), tangent friction (red lines), and cohesion (y-intercept of red lines) are determined. Lower gray dashed line represents steady-state sliding stress conditions; upper black dashed line represents stress conditions at failure. Figure reproduced from [91] with permission.

Figure 4. (a) Schematic diagram of restrengthening or secant friction evolution during slide-hold-slide (SHS) tests. (b) Diagram showing how secant friction (blue lines), tangent friction (red lines), and cohesion (y-intercept of red lines) are determined. Lower gray dashed line represents steady-state sliding stress conditions; upper black dashed line represents stress conditions at failure. Figure reproduced from [91] with permission.

4. Velocity Dependence Behavior Explained Using Microphysical Model

To describe the frictional behaviour of granular fault materials, Chen, Niemeijer, and Spiers developed a microphysical model (CNS) [42,73,74,75]. This model attributes friction to two key factors: porosity and grain boundary friction. It captures how velocity-dependent transitions arise from the competition between porosity generation via granular flow and porosity reduction via time-dependent, thermally activated creep processes. In the CNS framework, the rates of change of shear stress (τ), porosities of shear band (${\phi }^{sb}$), and bulk gouge (${\phi }^{bulk}$) are described by:

$$V_{imp}-\dot{\tau }/K=L_t\left[\lambda {\dot{\gamma }}_{ps}^{sb}+\left(1-\lambda \right){\dot{\gamma }}_{ps}^{bulk}\right]+L_t\lambda {\dot{\gamma }}_{gr}^{sb}$$

(6)

$$\tau =\overline{\sigma }{\displaystyle \frac{\tilde{\mu }+tan\phi }{1-\tilde{\mu }tan\phi }}$$

(7)

$${\dot{\phi }}^{sb}/\left(1-{\phi }^{sb}\right)=tan\phi {\dot{\gamma }}_{gr}-{\dot{\epsilon }}_{pl}^{sb}$$

(8)

$${\dot{\phi }}^{bulk}/\left(1-{\phi }^{bulk}\right)=-{\dot{\epsilon }}_{pl}^{bulk}$$

(9)

Here, $V_{imp}$ represents the velocity imposed at the loading point, and the gouge layer has a thickness of $L_t$, with a shear strain localizing within a fraction $\lambda$ of that thickness. The dot notation indicates a time derivative. Granular flow (gr) is assumed to be confined to the localized shear zone with a width of $L_t \lambda$, whereas intergranular plastic creep (pl) is considered to occur both inside this localized region and throughout the remaining bulk gouge material, covering a thickness of $L_t\left(1-\lambda \right)$. The dilatancy angle is denoted by $\phi$. Superscripts “sb” and “bulk” refer to the shear band and surrounding bulk material, respectively. Shear strain and normal strain are indicated by γ and ε. The frictional resistance at grain boundaries, represented by $\tilde{\mu }$, depends on the strain rate associated with the granular flow within the shear band.

Figure 5 shows a schematic diagram outlining the three distinct temperature-dependent regimes in terms of the velocity-dependence parameter. This schematic links the apparent friction coefficient and its velocity dependence to the underlying micro-mechanical deformation mechanisms proposed by the model. In Regime I, deformation is characterized by significant grain size reduction and a cataclastic flow involving quartz, albite, and K-feldspar, without any microstructural evidence for the creep or mass transfer processes, consistent with model A in Figure 5. For Regime II, the microstructures indicate a more distributed deformation pattern with multiple sharp Y-shears, in contrast to the localization observed in Regimes I and III. While cataclastic processes remain active, features such as grain-to-grain indentation and grain truncation, particularly within ultrafine-grained zones, suggest that pressure solution mechanisms began to operate, likely triggered by grain size reduction [79]. This regime reflects the interplay between dilatant granular flow and solution-assisted deformation, in line with model B of Figure 5. In Regime III, the presence of active B-shear bands containing ultrafine, equant grains of quartz, albite, and K-feldspar—accompanied by intergranular pores or healed cavities with low overall porosity and lacking shape-preferred orientation (SPO)—indicates a shift towards grain boundary sliding assisted by solution–precipitation creep and pore healing [73]. These characteristics support a deformation mechanism involving granular flow coupled with enhanced diffusive mass transfer, as illustrated by model C in Figure 5.

Under hydrothermal conditions, the extended CNS model provides a more physically consistent explanation of frictional behavior than classical RSF laws. It captures three velocity-dependent regimes—strengthening at low temperatures, weakening at intermediate temperatures, and restrengthening at high temperatures—by accounting for competing deformation and healing mechanisms (Figure 6). Unlike RSF or empirical flow laws, CNS incorporates the effects of slip velocity, effective normal stress, and evolving microstructures, such as porosity, grain size, and shear band thickness. These features make it well-suited for interpreting experimental observations of granite gouges across a range of temperatures and velocities [92].

5. Implications for Nucleation of Continental Earthquakes

It has long been known that earthquake activity is a symptom, if not the agent, of active tectonics. The cyclic nature of earthquakes, as described by Reid [22], depends on the schizosphere, plastosphere, and asthenosphere. This coupling of mechanical processes across these distinct layers influences the timing and magnitude of seismic events. Three primary models of strain accumulation exist, each differing significantly in how the schizosphere and plastosphere are coupled and their relative strengths. In the viscoelastic coupling model, the fault traverses the schizosphere but does not extend into the plastosphere, which is modeled as a viscous layer [95,96]. However, the strong plastosphere model suggests the fault is weak, and the plastosphere is strong; in that case, the plastosphere drives all systems during interseismic processes [97]. In the deep slip model, the fault may be active through both the schizosphere and plastosphere, being seismogenic in the schizosphere and aseismically slipping in a ductile shear zone, weaker than the bulk plastosphere, in the lower crust. In this model, the deep shear zone loads the schizosphere during the interseismic period, and the deeper zone is subsequently reloaded by the coseismic slip [98]. The deep slip model explored by Tse and Rice [99] not only provides more comprehensive details than earlier formulations but also accounts for several key characteristics documented in prior studies. This model investigated how the slip is distributed throughout repeated loading cycles on a fault governed by the RSF law (Equations (1)–(4)), using parameters derived from laboratory experiments. The values they used for the velocity dependence friction term (a − b), with the temperature gradient they assumed, predict a transition to a stable slip at 11 km (as (a − b) values transition from negative to positive) (Figure 7).

To our knowledge, the formation of seismological zones is linked to the thermomechanical and hydrological conditions within the lithosphere. Variations in temperature (T), normal stress (${\sigma }_n$), slip rate (V), shear displacement (S), and pore fluid pressure (P_f) can significantly alter the mechanical properties and rheological behavior of both the brittle upper crust (schizosphere) and the underlying ductile lower crust or upper mantle (plastosphere). The experimental results on quartz-rich and granitic gouges indicate that with increasing Ts, fault slips exhibit VW behavior ((a − b) < 0) at intermediate Ts (~100–400 °C), corresponding to mid-crustal depths (~4–16 km), suggesting stable slips for earthquake nucleation. In contrast, at both lower and higher Ts, the fault shows VS behavior ((a − b) > 0), indicative of stable sliding (Figure 5, A). However, the T range of the intermediate VW regime is not fixed; increasing the V tends to shift the transition from the VW to VS regime toward higher Ts (Figure 5, A). This is likely due to the reduced time available for thermally activated deformation mechanisms at higher strain rates. In contrast, elevated P_f facilitates all three frictional regimes toward lower Ts (Figure 5, B), a result consistent with the reduction in effective normal stress and hence frictional resistance. Furthermore, increasing cumulative slip allows more time for grain-scale deformation processes such as pressure solutions and ductile creep to operate, promoting a rheological transition from brittle to plastic behavior. These findings underscore the complex interplay among T, P_f, V, and S in controlling the micromechanical processes governing fault strength and stability (Figure 5, C).

Elevated pore fluid pressure is widely recognized as a critical factor in fault weakening and the initiation of unstable slip, thereby serving as a potential trigger for earthquake nucleation. In continental settings, numerous studies have demonstrated a strong correlation between high fluid pressure zones and seismogenic fault segments, particularly in regions such as the Tibetan Plateau and the North China Craton, where deep crustal fluids are actively involved in fault zone dynamics. Advances in microstructural analysis, including transmission electron microscopy (TEM) and synchrotron-based X-ray imaging, have revealed fluid-assisted grain boundary weakening, pressure solution features, and enhanced mineral reaction kinetics at asperity contacts under high fluid pressure conditions. These microscale observations provide compelling evidence that elevated pore fluid pressure facilitates the activation of ductile deformation mechanisms and reduces effective normal stress, thus promoting the transition from stable to unstable sliding. As such, incorporating fluid–rock interaction processes into fault mechanics models is essential for a more realistic understanding of earthquake nucleation in continental lithosphere. Future work should aim to bridge the gap between laboratory-derived frictional behavior and field-scale observations, with a particular focus on the spatiotemporal evolution of pore pressure and its role in modulating fault slip behavior across the seismic cycle.

6. Conclusions

This study provides a comprehensive synthesis of the frictional behavior of granitic faults, integrating key insights from theoretical frameworks and experimental observations. We first reviewed the classical rate-and-state friction (RSF) law, establishing its foundational role in modeling fault dynamics. Through a systematic comparison of dry and hydrothermal experiments on granitic fault gouges, we highlight distinct frictional responses (velocity-stepping, constant-velocity, and slide-hold-slide tests) under varying conditions. Our analysis emphasizes the critical roles of temperature, normal stress, pore fluid pressure, and slip velocity in modulating friction strength and sliding stability, revealing how these parameters interact to govern fault behavior across different regimes. Notably, we demonstrate that microstructural evolution—such as grain size reduction, pressure solution, and fluid-assisted healing—acts as a key mechanism driving transitions between velocity-weakening and velocity-strengthening regimes, with direct implications for earthquake nucleation and arrest. The key conclusions drawn are as follows:

(1)

Granitic faults in the crystalline upper-to-middle continental crust represent key structures controlling the seismogenic behavior and long-term deformation of the continental lithosphere. Their frictional properties are thus central to understanding earthquake initiation and rupture dynamics.

(2)

Laboratory friction experiments, including velocity-stepping (VS), constant-velocity (CV), and slide-hold-slide (SHS) protocols, consistently demonstrate that granitic gouges exhibit measurable and reproducible frictional behavior. Notably, the VS tests reveal frictional stability regimes (velocity-strengthening or -weakening), while SHS tests provide quantitative estimates of fault healing and restrengthening during interseismic periods.

(3)

Microstructural observations indicate that shear deformation induces localized shear, significant grain size reduction, pressure solution creep, and mineralogical alteration within the fault gouge. These microphysical processes are sensitive to temperature, normal stress, pore fluid pressure, and strain rate and play a pivotal role in modulating the rheology and frictional response of the fault zone.

(4)

In the continental crust, the interplay between microstructural evolution and frictional properties suggests that nucleation is favored in zones where brittle–frictional weakening mechanisms dominate but are bounded by ductile, velocity-strengthening regions that arrest rupture.