Frictional Characteristics of Granite Fault under Imposed Dynamic Normal Disturbance Loads

Dynamic disturbance loads resulting from natural phenomena or human activities, including earthquakes, earth tides, excavation, cyclic hydraulic fracturing, and blasting, are frequently encountered in the field of rock engineering projects. These loads might alter the motion state and frictional properties of geological faults, ultimately leading to the reactivation of these faults, characterized by fault slip. Fault reactivation, in this context, refers to the process in which a previously stable geological fault resumes slipping, resulting in instability and the generation of seismic activity. In most cases, fault reactivation poses a significant threat to the stability and safety of engineering projects. This is due to the fact that fault slip can release a large amount of energy and trigger severe dynamic geological disasters, such as fracturing and rockbursts, as documented in studies [1-5]. Conversely, fault reactivation can also be beneficial and essential for hydraulic fracturing projects aimed at enhancing the productivity of deep oil and gas reservoirs [6, 7]. In order to ensure the safety of specific rock engineering projects situated in proximity to faults and to enhance the efficiency of hydraulic fracturing endeavors, it becomes imperative to gain a comprehensive understanding of the dynamic mechanisms that trigger fault activation under the influence of dynamic disturbance loads.

Understanding the triggering mechanism of faults involves two critical aspects: frictional behaviors encompassing shear strength, sliding mode, and stability changes, as well as activation characteristics [8-10]. Previous research has primarily concentrated on investigating the frictional behaviors of faults under dynamic disturbance loading conditions. In these studies, faults were subjected to either a constant or varying shear rate, and dynamic changes in velocity or load were imposed on their initial state [11-15]. Consequently, displacement-driven shear tests under dynamic disturbance loading, encompassing dynamic normal stress, instantaneous normal stress step increases/decreases, slip-pulses, dynamic shear velocity, and dynamic shear stress, have been widely conducted. These investigations have unveiled the effects of dynamic disturbance load, shear velocity, and normal stress on shear strength, sliding behavior, and stability changes [16-22]. A noteworthy contribution to this field is the introduction of a novel model for assessing dynamic shear strength by Okada and Naya [23], which is based on one-way and two-way cyclic shear load tests. Furthermore, Liao et al. [24] conducted experimental analyses to examine frictional evolution under slip-pulses simulating large earthquakes. They compared these findings with those obtained from loading modes involving constant velocity and changing velocity. These studies have significantly advanced our comprehension of earthquake triggering mechanisms.

While extensive research has been devoted to understanding frictional behaviors, less attention has been paid to the activation characteristics of faults under dynamic disturbance loading, despite the potential practical significance of these characteristics in rock engineering projects. In such scenarios, faults typically exist in specific normal and shear stress environments and remain in a stable state before experiencing dynamic disturbance loading. This is followed by the imposition of dynamic changes in load to investigate the activation characteristics [25, 26]. To address this gap, researchers have conducted dynamic disturbance shear tests, where faults were initially subjected to preset normal and shear stress conditions. Subsequently, dynamic disturbance loads were applied in a random direction relative to the shear plane to assess fault activation. Ji et al. [3] conducted experimental investigations into unloading-induced rock fracture activation, which is a specialized case of dynamic disturbance loads associated with oil and gas extraction. They also proposed a method for predicting maximum seismic moments. However, it is worth noting that systematic studies on imposed dynamic disturbance shear tests for fault activation under specific stresses and dynamic disturbance loading have been scarce.

Seismic evidence and friction theory suggest that the triggering of fault instability and activation predominantly hinge upon the fault’s initial stress and the nature of dynamic disturbance loads [27-29]. In general, fault activation is more likely to occur when the initial stress approaches the static shear strength [30]. This implies that increasing the initial shear stress or reducing the initial normal stress promotes the slip instability of natural faults. Concerning dynamic disturbance loads, both amplitude and frequency have an impact on fault stability. Higher disturbance amplitudes tend to lead to fault instability. However, contradictory findings regarding the effect of disturbance frequency on fault instability have been reported [28]. It is essential to underscore that the aforementioned conclusions are drawn from studies on the frictional behaviors of faults based on displacement-driven shear tests under imposed dynamic disturbance or unloading normal load conditions. The effects of initial normal stress, initial shear stress, disturbance amplitude, and disturbance frequency on fault activation characteristics remain unclear.

The primary objective of this study is to elucidate the activation characteristics exhibited by laboratory faults when subjected to specific stresses and dynamic disturbance loading. Furthermore, it seeks to explore the influence of factors such as initial normal stress, initial shear stress, disturbance amplitude, and disturbance frequency on the initiation of fault activation. To achieve this aim, we utilized a saw-cut bare granite surface as a representation of a natural fault and employed cyclic sine stress to mimic seismic disturbance loading conditions within a laboratory setting. Imposed dynamic disturbance shear tests were conducted on these simulated faults, encompassing various initial shear stresses and cyclic sine stresses. In this article, we present and discuss some preliminary findings derived from these tests. The outcomes of this research endeavor are anticipated to contribute significantly to our comprehension of the dynamic processes that trigger fault activation.

In our laboratory experiments, we employed a saw-cut bare granite surface to mimic a natural fault plane [31, 32]. The dimensions of the upper and lower granite blocks were 300 mm × 150 mm × 100 mm (Length × Width × Height) and 400 mm × 150 mm × 100 mm, respectively. This arrangement allowed us to maintain a consistent fault area of 0.045 m² for the simulated fault throughout the testing process. This design effectively minimized any inhomogeneous stress distribution on the fault plane that might arise from the rotation of the upper specimen during direct shear tests. It was polished on all surfaces using a 150-mesh red grinding wheel to ensure its smoothness and uniformity. The principal mechanical properties of granite are determined through a series of standard tests, including the uniaxial compression test, the Brazilian splitting test, the tilt test, and the direct shear test. The results obtained from these tests are as follows: the uniaxial compressive strength is measured at 225.13 MPa, the elastic modulus is 53.47 GPa, the Poisson’s ratio is 0.20, and the indirect tensile strength is 12.60 MPa. Additionally, for the saw-cut bare granite surface, the static friction coefficient is 0.82, while the cohesion is negligible at 0 MPa.

A newly self-developed multifunctional shear test apparatus for rock discontinuity under dynamic disturbance loading (Type: DDST-1800) was used to investigate the activation characteristics of simulated fault under imposed normal stress disturbance. DDST-1800 has the functions of static loading, dynamic loading, and impact loading. The static loading capacities were up to 1800 kN in both normal and shear directions. Regarding dynamic loading, a maximum disturbance load of 200 kN and a disturbance frequency of 50 Hz can be realized in the normal direction, and a maximum disturbance frequency of 20 Hz can be applied in the shear direction. A pendulum hammer-driven impact system is used to apply impact loading, where the initial position of the pendulum hammer can be adjusted within 0–135°, the weight of the pendulum hammer is 100 kg, and the weight and length of the pendulum rod are 31.27 kg and 1.8 m, respectively. Static, dynamic, and impact loads and displacements along both normal and shear directions are recorded in real time. More information about DDST-1800 can refer to Cui et al. [33].

In the imposed dynamic disturbance shear tests, we initiated the experiment by loading the simulated fault to a specific shear stress ratio. This ratio is defined as the ratio of the shear stress to the corresponding static shear strength under a particular normal stress condition. Subsequently, dynamic normal disturbance loads were applied (as illustrated in Figure 1) to investigate the activation characteristics of the faults. This setup aligns with methodologies from prior studies [22], which imposed normal stress variations to explore fault slip and frictional weakening, but unlike those focused primarily on fault gouge, our research targets the fault plane itself. In these tests, the initial normal and shear stress ranges were determined with reference to the works of Dang et al. and Yamashita et al. [16, 34], where the initial normal stresses ranged from 1.33 MPa to 2.22 MPa, and shear stresses ranged from 0.67 MPa to 0.78 MPa. The applied normal stresses correspond to depths within 200 meters, calculated using horizontal and vertical in situ stress formulas provided by Brown & Hoek [35], along with considerations of fault dip and other relevant factors. However, it is important to note that the stress levels used in this study are relatively low, which constitutes a limitation of the current work. Correspondingly, the initial shear stress ratios ranged from 0.43 to 0.72, as outlined in Table 1. To mimic seismic disturbance loads, we employed cyclic normal sinusoidal stresses, representing a simplified form of imposed dynamic normal disturbance loads. This approach is akin to the one utilized by Dang et al. [16]. For the cyclic sinusoidal stresses, the test began with an incremental phase, with a cycle period set at 100. The amplitudes of these stresses were set at 0.33 MPa, 0.67 MPa, and 1 MPa, which fall within a reasonable range for dynamic disturbance loading on frictional faults based on the previous experimental studies [4, 36]. Typically, the frequency of seismic loads falls within the range of 0–20 Hz [37]. However, the effect of disturbance frequency on fault activation had been relatively unexplored under specific initial shear stress ratios and imposed dynamic disturbance loads. Consequently, we considered disturbance frequencies of 1 Hz, 5 Hz, 10 Hz, and 20 Hz to elucidate the impact of loading frequency in this context. Regarding the dynamic disturbance parameters, it is not intended to represent specific subsurface conditions but rather to simulate the general effects of dynamic loading on the frictional characteristics of the simulated fault. Throughout the testing process, we meticulously captured real-time load and displacement data along both the normal and shear axes at a sampling frequency of 1000 Hz. This high-frequency monitoring was facilitated by Linear Variable Differential Transformers and load cells that were integrated into the loading actuator, ensuring precise tracking of both stresses and displacements throughout the experiment. This comprehensive data collection allowed for a detailed analysis of the activation characteristics of the fault under different conditions.

In our study, we categorized faults into two distinct states: “inactivated” and “activated.” Inactivated and activated faults denote the stable and sliding faults after dynamic normal disturbance loading in the context, respectively. The mechanical and deformation responses of the simulated faults were found to be contingent on their state, and similar responses were observed under different initial stress ratios and normal disturbance loading conditions when the fault state remained consistent. Figure 2 illustrates the characteristic evolution patterns of shear stress, apparent friction coefficient (shear stress vs. normal stress), shear displacement, and normal displacement exhibited by the simulated fault under dynamic normal disturbance loading. The shear stress behavior observed under dynamic normal disturbance loading in our experiments exhibits characteristics similar to those reported by Dang et al. [16], further validating our experimental results. In this specific case, the shear stress ratio is 0.72, and the disturbance amplitudes ranged from 0.33 MPa to 1 MPa. The initiation time of the imposed normal sine stress was consistently set at approximately 1 second in all figures. Notably, the variation in shear displacement depicted in Figure 2 indicated that under a disturbance amplitude of 0.33 MPa, the simulated fault remained inactivated. However, when subjected to disturbance amplitudes of 0.67 MPa and 1 MPa, the fault became activated, signifying the slip occurred. This observation suggests that external dynamic normal disturbance loads have the potential to trigger the dynamic failure of natural faults.

Figure 3 provides a graphical representation of the changes in shear stress, apparent friction coefficient, and shear displacement in response to disturbance normal loads for both inactivated and activated faults. For the inactivated fault, it is evident that a nearly regular and periodic pattern of oscillations occurs in shear stress, apparent friction coefficient, and shear displacement when subjected to periodic fluctuations in normal stress, excluding the first cycle where slight slip existed due to unloading. The frequency of these oscillations closely aligns with that of the dynamic normal disturbance load. In general, both shear stress and shear displacement exhibit similar trends to the oscillations in normal load, while the apparent friction coefficient behaves in the opposite manner. An interesting observation is the presence of a phase lag phenomenon between shear stress (or displacement) and normal stress, similar results were observed by Cui et al. although our tests employed a relatively low disturbance frequency [38].

In the case of the activated fault, the behavior of shear stress, apparent friction coefficient, and shear displacement also displayed a periodic pattern, with the exception of the first cycle. Notably, during the first cycle, there was a noticeable and unrecoverable drop in shear stress, which implied that the slip changed the frictional properties of the fault. This phenomenon can be attributed to the sudden change in the kinematic state of the simulated fault. A similar stress drop was observed in the work of Konietzky et al. in the context of rock fracture under dynamic disturbance loading [25]. Following this initial cycle, the behavior became nearly periodic. An intriguing finding is that within each cycle, the simulated fault exhibited an initial slow slip followed by a subsequent rapid slip. This pattern closely resembles the stick-slip events commonly observed in displacement-driven shear tests of faults. These results underscore the idea that the imposed dynamic normal disturbance on initially stable faults has the potential to induce dynamic instability in the fault system.

Figure 3 also includes key parameters used to quantify the responses of the laboratory fault under dynamic normal disturbance loading. Here is a brief explanation of these parameters: ∆τ and ∆f represent the range of variation in shear stress and apparent friction coefficient during one normal stress cycle, respectively. d is referred to as slip displacement in one stick-slip event. f_p and f_v are the apparent friction coefficients in the peak and valley, respectively. τ_p and τ_v are the peak and valley shear stresses, respectively. Figures 4-6 provide insights into the effects of initial normal stress, initial shear stress, disturbance amplitude, and disturbance frequency on these main quantified parameters of the simulated fault under dynamic normal disturbance loading. The presented values are averaged for clarity and ease of interpretation.

For the inactivated fault, it is noteworthy that the peak shear stress exceeds the initial shear stress, whereas for the activated fault under the tested amplitudes (as depicted in Figure 4(a)), the peak shear stress becomes smaller than the initial value. This observation indicates a dynamic weakening in the shear strength of the simulated fault induced by the disturbance load. The peak shear stress demonstrated a decreasing trend as the disturbance amplitude increased, implying that dynamic weakening becomes more pronounced with larger amplitudes.

The peak apparent friction coefficient of the simulated faults exhibits an interesting behavior, initially increasing and then decreasing. Specifically, under disturbance amplitudes of 0.33 MPa, 0.67 MPa, and 1.00 MPa, the peak apparent friction coefficients were 0.72, 0.74, and 0.67, respectively. This phenomenon is linked to the kinematic state of the simulated fault. At lower disturbance amplitudes, the peak apparent friction coefficient is lower than the peak friction coefficient, indicating that the fault remains stable. The peak value gradually increases with the disturbance amplitude until the fault becomes activated. Subsequently, the peak apparent friction coefficient decreases with further increases in disturbance amplitude, primarily due to the ultra-low friction mechanisms coming into play. Moreover, both ∆τ and ∆f tend to increase as the disturbance amplitude rises. Additionally, the slip displacement d also increases with higher disturbance amplitudes. Consequently, larger disturbance amplitudes can lead to more severe dynamic failure in the fault system.

Figures 4-6 demonstrate that fault activation occurred in all cases within Set B, and the primary quantified parameters were notably dependent on the disturbance frequency. As the disturbance frequency increased, the peak shear stress exhibited a gradual decline trend, with the rate of decrease becoming more pronounced. The valley shear stress, on the other hand, showed relatively minor changes when the disturbance frequency remained within 10 Hz but decreased significantly when the disturbance frequency increased from 10 Hz to 20 Hz. This observation suggests that higher disturbance frequencies have the potential to induce more pronounced dynamic weakening in the fault system. Moreover, it is apparent that the peak friction coefficient closely approached the static friction coefficient under low-frequency disturbance conditions, such as 1 Hz and 5 Hz (refer to Figure 5(b)). However, under high-frequency disturbance (>5 Hz), the peak friction coefficient was consistently smaller than the static friction coefficient.

In specific terms, the peak friction coefficient f_p tended to decrease with increasing disturbance frequency. For instance, the values of f_p were 0.79, 0.8, 0.73, and 0.39 under disturbance frequencies of 1 Hz, 5 Hz, 10 Hz, and 20 Hz, respectively. This trend can be attributed to the direct response of normal displacement, which increases with disturbance frequency. Larger normal displacement leads to a more significant reduction in frictional resistance in the simulated faults, particularly when the upper and lower specimens exhibit loose contact. Furthermore, the valley apparent friction coefficient f_v also decreased with increasing disturbance frequency. The slip displacement d initially decreased as the disturbance frequency increased from 1 Hz to 10 Hz, but it subsequently increased once the disturbance frequency exceeded 10 Hz. In summary, it appears that high-frequency normal disturbance is more effective at triggering fault activation.

The behavior of the fault varied depending on the initial normal stress conditions. Specifically, under initial normal stresses of 1.33 MPa and 1.78 MPa, the fault was activated, exhibiting slip. In contrast, when subjected to an initial normal stress of 2.22 MPa, the fault remained stable and did not undergo activation. As the initial normal stress increased, fault activation was suppressed, and there was a transition from activation to inactivation. Both the peak and valley shear stresses increased with higher initial normal stress. Regarding the peak apparent friction coefficient f_p, it exhibited an initial increase for activated faults and then decreased when the fault transitioned from activation to inactivation. In contrast, the valley apparent friction coefficient f_v increased regardless of whether the fault was in an activated or inactivated state (as shown in Figure 5(c)). Additionally, the slip displacement d decreased when higher initial normal stress was applied.

Figure 7 illustrates the impact of initial shear stress on fault activation characteristics under dynamic normal disturbance loading, with a frequency of 10 Hz, an amplitude of 0.67 MPa, and a cycle duration of 100. In this scenario, the initial normal stress is set at 1.33 MPa, and different initial shear stresses of 0.67 MPa, 0.72 MPa, and 0.78 MPa are considered. Here are the key observations: Fault activation was observed in all cases. Higher initial shear stress favored fault activation, and the onset of slip may be delayed as the initial shear stress decreases. A transition from a steady state to activation might occur as the cycle duration increases at certain shear stress. This implies that cumulative disturbance can weaken the mechanical properties of the simulated fault, leading to relative slip. Under an initial shear stress of 0.67 MPa, two activation phases were captured at the 8th and 21st cycles, with the simulated fault returning to a steady state after each activation phase. Under an initial shear stress of 0.72 MPa, continuous fault activation was observed after the 35th cycle. Under an initial shear stress of 0.78 MPa, continuous fault activation occurred from the first cycle. As the initial shear stress increased, the simulated fault tended to be activated. For the activated faults, the variation in peak and valley shear stresses and apparent friction coefficients was relatively small, while the slip displacement d increased gradually.

As shown in , the simulated fault displayed stick-slip characteristics when subjected to imposed dynamic normal disturbance loading. The difference in the evolution of shear displacement between the displacement-driven test, and this test primarily lies in the following aspects: (1) During the stick stage, shear displacement increases slowly in the displacement-driven test because the fault is continuously forced forward. In contrast, in this test, shear displacement changes relatively less during the stick stage because the fault remains static; (2) Stick-slip events in the displacement-driven test typically feature a longer stick stage than a slip stage. In contrast, in this test, the durations of the stick stage and slip stage are similar because of the oscillatory nature of the normal stress applied to the fault.

Figure 8 presents the shear stress and apparent friction coefficient versus shear displacement curves of the simulated fault under dynamic normal disturbance loading, with initial normal and shear stresses set at 1.33 MPa and 0.78 MPa, and a disturbance amplitude of 1 MPa. In the stick stage, there is minimal variation in shear displacement. The apparent friction coefficient increases rapidly to its peak value, while shear stress declines from its peak to the valley. In the slip stage, shear displacement increases rapidly. During this phase, the apparent friction coefficient decreases from its peak to the valley, and shear stress gradually rises to its peak. Notably, the evolution of the apparent friction coefficient under imposed normal disturbance loading aligns with the behavior observed in displacement-driven shear tests. However, the trend in shear stress is opposite; in displacement-driven shear tests, shear stress increases in the stick stage and decreases in the slip stage. This difference can be attributed to the dynamic and constant normal stress boundaries in the two testing conditions.

The peak apparent friction coefficient exhibits variability with respect to disturbance amplitude, frequency, and initial stress ratio, as illustrated in Figure 5. Among these factors, disturbance frequency exerts a more pronounced influence on the peak apparent friction coefficient compared to the others. Figure 9 provides a visual representation of the variation of the peak apparent friction coefficient with disturbance frequency, and it includes results reported by Cui et al. [38]. When the disturbance frequency is lower than 5 Hz, the peak apparent friction coefficient is nearly equal to the static friction coefficient. As the disturbance frequency increases beyond 5 Hz, the peak apparent friction coefficient gradually declines. This trend in the evolution of the peak friction coefficient could potentially be explained using rate and state friction laws, although further detailed studies are planned for the future to investigate this phenomenon more comprehensively.

The experimental findings offer valuable insights with potential engineering implications. Despite the differences between laboratory-scale and field-scale conditions, the fundamental frictional and slip processes observed on the saw-cut surface reflect general fault mechanics, allowing us to draw conclusions that are applicable to large-scale faults. For the fault adjacent to excavation, the results suggest that dynamic normal disturbance loads have the potential to trigger the instability and activation of preexisting faults, especially under high-frequency disturbance loads. This observation provides an explanation for phenomena like fault-slip rockbursts. To reduce the risk of fault activation, it may be advisable to decrease the magnitude of high-frequency disturbance loads. Moreover, the static friction coefficient can serve as a useful indicator for assessing the shear strength of a fault when the disturbance frequency is within 5 Hz. However, when the disturbance frequency exceeds 5 Hz, a lower friction coefficient should be considered for accurate assessments. As for cyclic hydraulic fracturing, it is an effective technique for enhancing the productivity of deep oil and gas reservoirs. The results suggest that increasing the disturbance frequency reduces the fracture's friction coefficient, making natural fractures are more prone to slippage and shear failure, thereby improving reservoir performance. These insights can be valuable in engineering and geological assessments, helping to mitigate risks and optimize the outcomes of projects involving faulted geological structures and dynamic disturbance loads.

The slip mechanisms of the simulated fault under dynamic normal disturbance loads are exceedingly intricate and have been preliminarily explained using several mechanical models, including the Mohr-Coulomb strength criterion, rate and state friction law, and slip weakening friction law [39, 40], as illustrated in Figure 10. Prior to the application of disturbance loading, the shear stress on the fault is less than the static shear strength, and the fault remains stable. As the normal disturbance load is progressively applied, the shear stress gradually approaches the shear strength, and the fault initiates slip when the stress point reaches the failure envelope under a specific disturbance load. It is essential to emphasize that the failure envelope undergoes offsetting under the influence of dynamic normal disturbance loads, contributing to the complexity of the slip mechanisms observed in the experiments.

Following the initiation of fault slip, dynamic instability ensued, and the shear displacement of the simulated fault rapidly increased, following the principles of the slip-weakening friction law. The slip motion would come to a halt when the simulated fault returned to the stick stage due to variations in normal stress. During this phase, the friction coefficient of the simulated fault would promptly recover to its peak value. Subsequently, a cycle of repeated stick-slip events of the simulated fault would occur. This behavior is consistent with the observed stick-slip characteristics previously described.

This study delved into the evolution characteristics of stress, apparent friction coefficient, and displacement for both inactivated and activated faults under specific stress conditions and imposed dynamic normal disturbance loads. It subsequently unveiled the impacts of disturbance amplitude, disturbance frequency, initial normal stress, and initial shear stress. The key findings and conclusions can be summarized as follows:

• Imposed dynamic normal disturbance loads have the potential to trigger the activation of simulated faults, and this activation is influenced by the initial static stress ratio and disturbance parameters. A transition from inactivation to activation occurs with variations in disturbance amplitude, frequency, cycles, and initial stress ratio. In general, fault activation is more likely to occur under conditions of higher disturbance amplitude and frequency, lower initial normal stress, and larger initial shear stress.

• Periodic dynamic normal stress induces approximate regular oscillations in shear stress, apparent friction coefficient, normal displacement, and shear displacement for both inactivated and activated faults. The oscillation frequency closely aligns with that of the dynamic normal load.

• For activated faults, a stick-slip characteristic is observed in each disturbance cycle. Disturbance frequency has a more pronounced influence on the peak friction coefficient compared to disturbance amplitude and initial stress ratio. Under low-frequency disturbance conditions, the peak friction coefficient of activated faults approaches the static friction coefficient, whereas it significantly deviates from the static friction coefficient under high-frequency disturbance conditions.

• Slip displacement of activated fault tended to increase with disturbance amplitude, initial shear stress, decrease with initial normal stress, and increase first and then decrease with disturbance frequency.

Some or all data used are available from the corresponding author by request.

The authors have declared that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work.

This research was funded by the National Natural Science Foundation of China, grant numbers 52109142 and 52279116.