Preamble

Thermal Effect on Nano-Scale Sliding Friction of Fault Gouge

Guojun Sun, Dongya Han
School of Resources and Safety Engineering, Central South University, Changsha 410083, China

Abstract

Fault slip behavior is key to understanding the mechanisms of earthquake nucleation and rupture. In nature, due to friction and wear caused by fault activity, faults mostly exist in the gouge-bearing form, whose frictional properties are controlled by their mineral composition and temperature conditions. To investigate the influence of temperature on fault slip mechanisms, this study employs the steered molecular dynamics (SMD) method based on the CLAYFF force field, conducting friction simulations under a constant shear rate (100 m/s). The slip behavior of a quartz-kaolinite-quartz system was analyzed within the temperature range of 200 K-500 K, with the influence mechanism of kaolinite as a weak-phase mineral on the frictional properties of gouge-bearing faults being investigated. Through examination of the friction process, shear stress, friction coefficient, and interfacial interactions, the regulatory effects of temperature on the slip behavior of fault gouge were revealed, leading to deeper insights into the weakening phenomenon of fault mechanical properties under high-temperature conditions in deep geological environments. The research results indicate that there is a significant stick-slip effect at the friction interface, with the stick-slip effect becoming stronger as the normal load increases. The presence of clay minerals markedly reduces the frictional strength of quartz. The friction coefficient exhibits an inverse temperature dependence, where thermal fluctuations at elevated temperatures facilitate the system to overcome energy barriers, resulting in decreased steady-state frictional stress. These findings provide atomic-scale insights into the pressure-temperature coupling effects in clay-bearing faults.

Keywords: temperature effect; molecular dynamics; fault gouge; stick-slip

Introduction

Faults are widely distributed weak zones in the crust, and their slip behavior directly controls earthquake nucleation, rupture propagation, and energy release. Under natural conditions, long-term tectonic activity through friction and wear leads to the development of fault gouge composed of fine-grained minerals (such as clay and quartz) in most faults [1]. The mechanical properties of such clay-bearing faults differ significantly from intact rock, with frictional characteristics governed by mineral composition, temperature-pressure conditions, fluid environment, and other factors, among which temperature plays a particularly critical role. Experimental studies have demonstrated that temperature exerts significant regulatory effects on the frictional behavior of clay-bearing faults. For instance, natural fault gouge from the Longmenshan fault zone exhibits a decreasing steady-state friction coefficient with increasing temperature in the range of 25-150°C [2], whereas biotite-bearing fault gouge shows an increasing friction coefficient with temperature rise in the 25-600°C range [3]. Furthermore, elevated temperatures can promote plastic deformation of clay minerals, leading to reduced shear strength of fault gouge and even triggering dynamic weakening mechanisms. However, traditional experimental methods still face limitations under high-temperature and high-pressure conditions, such as difficulty in precisely controlling microstructures, inability to directly observe atomic-scale energy dissipation and interfacial interactions, and unclear temperature-pressure coupling mechanisms in high-speed friction experiments. Molecular dynamics simulations can reveal the microscopic regulatory mechanisms of temperature on fault slip through atomic-scale modeling. For example, Ying et al. [4] calculated the friction angle of montmorillonite at different temperatures, verifying that the increase in clay friction angle with temperature results from the loss of adsorbed water at high temperatures. Compared with kaolinite and illite, montmorillonite's shear properties are least affected by temperature, as water molecules in clay minerals move slowly at low temperatures, which to some extent increases shear resistance [5]. In contrast to experiments, molecular dynamics simulations can precisely specify mineral components and temperature-pressure conditions while directly calculating microscopic processes such as interfacial bonding and dislocation motion, providing new insights into understanding the thermomechanical weakening of clay-bearing faults.

This study employs the steered molecular dynamics method with the CLAYFF force field to simulate the shear behavior of quartz-kaolinite-quartz systems across the temperature range of 200-500 K. By analyzing friction evolution, friction coefficients, and interfacial interactions in clay-bearing faults, we explore the influence of high-temperature and high-pressure environments on the frictional properties of clay-bearing faults and provide molecular-scale evidence for the weakening mechanism of kaolinite as a weak-phase mineral that reduces fault slip resistance. Through analysis of how thermal fluctuations affect energy barrier crossing, we investigate the temperature dependence of clay-bearing faults and the evolution of their mechanical properties under deep high-temperature and high-pressure conditions. The research results will provide atomic-scale benchmarks for parameterizing earthquake physical models and advance multiscale modeling of fault friction constitutive relationships.

2.1 Model Construction

Quartz is one of the major rock-forming minerals, composed primarily of silicon dioxide. Kaolinite is a common constituent in many natural fault gouges and serves as an excellent representative of non-swelling clays. Therefore, a single layer of kaolinite supercell was employed to simulate fault gouge, while three layers of silica supercells were used to model the slider and substrate of the clay-bearing fault system. The unit cells for both minerals were obtained from the data models of Bish [6] and Antao [7], respectively. Both quartz and kaolinite were cleaved along the (001) crystal plane index, with oxygen atoms on exposed surfaces saturated by hydrogen atoms and silicon atoms saturated by hydroxyl groups. The quartz slider, kaolinite interlayer, and quartz substrate were assembled sequentially from bottom to top, yielding the clay-bearing fault model shown in Figure 1 FIGURE:1. A vacuum layer of 50 Å was set in the z-direction to avoid interactions between boundary atoms in this direction, resulting in final dimensions of 54.01×51.03×98.47 ų for the quartz-kaolinite-quartz system.

2.2 Force Field

The simulations were conducted using the CLAYFF force field [8] via the LAMMPS simulator. CLAYFF is specifically designed for modeling clay minerals and related materials, effectively characterizing the structure, properties, and behavior of hydroxides, oxyhydroxides, and clay phases, and is therefore widely employed in multi-component mineral system simulations. The total potential energy (Etotal) of the entire system comprises bond stretching energy (Ebond stretch), angle bending energy (Eangle bend), van der Waals energy (EVDW), and Coulombic electrostatic potential energy (ECoulomb):

$$E_{total}=E_{bond\ stretch}+E_{angle\ bend}+E_{VDW}+E_{Coulomb}$$

To ensure the compatibility of the CLAYFF force field with the quartz-kaolinite-quartz system, validation was performed for both kaolinite and quartz from three aspects: density, radial distribution functions before and after relaxation, and tensile strength. Quartz and kaolinite blocks with dimensions of 54.05×51.06×32.43 ų and 56.69×53.62×32.43 ų were constructed, respectively. The simulated densities of 2.649 g/cm³ and 2.608 g/cm³ closely match experimental values. The models were fully relaxed in the canonical (NVT) and isothermal-isobaric (NPT) ensembles to equilibrate them at 300 K and 1 atm. Figure 2 [FIGURE:2] presents the radial distribution functions for selected atomic pairs. The curves before and after relaxation show essentially identical trends, with probability peaks occurring at nearly the same positions along the distance axis, though with slightly increased intensities post-relaxation. This indicates that the relative distances between different atom types remain unchanged, and the crystal parameters and equilibrium configurations of both quartz and kaolinite remain stable under the CLAYFF force field. Uniaxial tension was applied by imposing a constant strain rate to the simulation box until a total strain of 0.3 was achieved. The resulting stress-strain curves are shown in Figure 3 [FIGURE:3], which agree well with previous studies using the same force field [9]. Therefore, the CLAYFF force field environment established in this study is considered effective for simulating the mechanical behavior of the quartz-kaolinite-quartz system.

2.3 Simulation Process

Fault slip was achieved using the spring-pull method via steered molecular dynamics (SMD). In the simulations, constant-velocity SMD was applied to pull the quartz slider horizontally, thereby simulating shear deformation. Periodic boundary conditions were employed in all three directions, with van der Waals interactions calculated using the Lennard-Jones potential and a cutoff radius of 10 Å. The Verlet algorithm was used for integrating the equations of motion, while the Ewald summation method was employed to compute long-range electrostatic interactions. The time step for all simulations was set to 1.0 fs.

To implement SMD simulations, both the slider and substrate were divided into three regions: boundary layer, thermostat layer, and Newtonian layer, as illustrated in Figure 1(c). The upper and lower boundary atoms were treated as rigid bodies without ensemble constraints. Throughout the simulation, the lower boundary atoms remained fixed at their initial positions, while the upper boundary atoms transmitted external loads applied to the system. The thermostat layer employed a Nose-Hoover thermostat to maintain the system at the target temperature. Atoms in the Newtonian layer could move freely, with the fault gouge contained within this layer.

Initially, the conjugate gradient method was used for energy minimization to obtain an equilibrium configuration of the quartz-kaolinite-quartz system. The thermostat and Newtonian layers were then equilibrated in the NVT ensemble for 200 ps at temperatures of 200 K, 300 K, 400 K, and 500 K, with a damping parameter of 100. Prior to friction simulations, the target normal load was applied to the model. The thermostat layer ensemble remained unchanged, while the Newtonian layer atoms and fault gouge were subsequently controlled using the microcanonical (NVE) ensemble for 200 ps. During constant-velocity SMD simulations, the mean square displacement of the quartz slider and spring force were monitored dynamically until the slider displacement reached 100 Å. By tracking the entire system motion, it was observed that both the quartz slider layer and kaolinite interlayer maintained stable uniform motion, indicating that the virtual spring force can effectively characterize the frictional force evolution during shear.

3.1 Friction Process

Figure 4 FIGURE:4-(e) illustrates the evolution of frictional force with sliding distance for the clay-bearing fault. The frictional force increases from zero, then fluctuates around a stable value, with its mean considered as the frictional force during fault slip. The frictional force gradually increases with normal stress. During normal stress application, stress is transmitted through the boundary atoms of the slider layer to the underlying structure, causing overall elastic or plastic deformation. As normal stress increases, the various components of the clay-bearing fault become more compact, the interlayer spacing gradually decreases, and the number of atoms participating in interfacial interactions increases, leading to stronger intermolecular forces. Consequently, frictional stress increases with applied normal load.

Analysis of average frictional forces under different normal loads reveals a linear relationship between shear stress and normal load stress, as shown in Figure 4 FIGURE:4, with the increasing trend following Coulomb's friction law. The friction coefficient is 0.037, which is consistent with previous simulation results for quartz-kaolinite systems [11] and pure kaolinite systems [12], and significantly smaller than that of quartz-quartz systems [11]. This demonstrates that the overall frictional strength of clay-bearing faults is influenced by the weaker kaolinite, with the presence of fault gouge manifesting as a weakening effect on rock fault frictional strength.

From an energy perspective, atomic stick-slip effects can be interpreted as processes of potential energy surface variation and energy dissipation. During the sticking phase, potential energy gradually accumulates; when sufficient energy is built up to overcome the energy barrier, slider atoms jump from their current stable position to the next, and the potential energy is suddenly released during the sliding phase, causing periodic fluctuations in frictional force [13]. The combined action of thermal fluctuations and applied stress enables atoms to overcome energy barriers, with thermal energy facilitating atomic sliding across barriers and allowing atoms to skip potential barriers. Therefore, higher temperatures promote easier sliding. As expressed in Equation (2), the thermally activated Prandtl-Tomlinson (PT) model predicts the relationship between friction, temperature, and velocity [14].

$$F = F_c - (\beta k_B T \ln($$

where F is the average frictional force, T is temperature, Fc is the critical frictional force independent of temperature, β is a measure of the potential corrugation curvature, kB is the Boltzmann constant, and v and vc are the sliding velocity and characteristic velocity, respectively.

Temperature and frictional force data under various normal loads were fitted according to Equation (2). The results are shown in Figure 7 [FIGURE:7]. Due to the small frictional force values at 1 GPa, the fitting error is relatively large with R² = 0.782. For other normal stress conditions, the fitted R² values all exceed 0.969. Therefore, the quartz-kaolinite-quartz model validates the temperature dependence of clay-bearing faults at the microscopic scale and follows the thermally activated PT model.

3.3 Main Sliding Surface Transition

The quartz-kaolinite-quartz system exhibits two sliding interfaces with different displacement magnitudes during slip, and the primary slip plane gradually transitions from the Si-O surface to the Al-OH surface of kaolinite with increasing normal stress. To investigate the factors influencing slip magnitude, the slider and substrate were fixed while the kaolinite layer was pulled at constant velocity using a virtual spring under various normal loads, maintaining identical interlayer spacing and normal load conditions as in the slider-pulling scenario. Measurements of frictional behavior at both interfaces revealed that at low normal stress, the Al-OH interface consistently exhibits higher frictional force than the Si-O surface, making the Si-O surface more prone to sliding. As normal stress gradually increases, the frictional force at the Si-O surface grows and eventually exceeds that of the Al-OH interface, causing a transition in the primary friction plane. Velocity measurements of each component during slider-pulling simulations show that the slider maintains a constant velocity of 100 m/s under spring traction, exerting a driving force on the kaolinite in the positive x-direction, while the fixed substrate layer provides a resisting force in the negative x-direction. Under these force conditions, the kaolinite adjusts its velocity to achieve force equilibrium and maintain uniform motion. Therefore, the difference in relative velocities between kaolinite and the slider/substrate is the direct cause of varying slip magnitudes at the two friction interfaces, while interatomic interaction forces constitute the fundamental factor controlling slip magnitude.

As shown in Figure 9 [FIGURE:9], under the same normal stress, higher temperatures result in lower sliding velocities of kaolinite. Measurements of kaolinite velocity under different normal stresses reveal that at 200 K, the normal stress corresponding to the primary slip plane transition occurs between 9 GPa and 10 GPa. For temperatures between 200 K and 600 K, the transition occurs between 8 GPa and 9 GPa, while at temperatures ≥600 K, the primary slip plane transitions from the Si-O surface to the Al-OH interface at stresses below 8 GPa. With increasing temperature, the critical normal stress for primary slip plane transition gradually decreases, indicating that high-temperature and high-pressure environments both favor slip along the Al-OH interface of kaolinite in clay-bearing faults.

In tribology, both Arrhenius theory and the PT model are used to explain temperature effects on frictional behavior. While the PT model is generally applicable at the microscopic scale, Arrhenius theory finds more application in macroscopic fault slip. Analysis of friction coefficients for the quartz-kaolinite-quartz system at different temperatures reveals a linear relationship between ln(μ) and 1/T, consistent with Arrhenius theory and further validating the intrinsic consistency of temperature effects on clay-bearing fault slip across microscopic and macroscopic scales. Figure 8 [FIGURE:8] illustrates the relationship between temperature and friction coefficient.

Conclusions

Through simulations of the quartz-kaolinite-quartz system slip behavior at 200 K, 300 K, 400 K, and 500 K, the influence of temperature on the friction mechanisms of clay-bearing faults was analyzed, yielding the following conclusions:

(1) Kaolinite, as a weak-phase mineral, exerts a weakening effect on rock fault friction, significantly reducing fault strength.

(2) Due to the degradation of rock mechanical properties and promotion of sliding at elevated temperatures, the average frictional force during slip of clay-bearing faults decreases with increasing temperature under the same normal stress.

(3) Under identical slip velocities, higher temperatures result in smaller friction coefficients for the quartz-kaolinite-quartz system, with ln(μ) exhibiting a linear relationship with 1/T.

(4) The frictional force of the quartz-kaolinite-quartz system demonstrates temperature dependence, with high-temperature conditions facilitating atomic sliding over potential energy barriers.

(5) The quartz-kaolinite-quartz system exhibits two friction interfaces (Si-O surface and Al-OH surface) during sliding. Larger normal stress and higher temperature both favor the Al-OH surface becoming the primary slip plane.

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