1 Introduction

Fault zones are commonly confronted in deep mining and geo-reservoir constructions. Seismogenic fault zones are comprehensive spatial–temporal regions, which are influenced by mineral types, fracture roughnesses and fluid lubrification (Carpenter et al. 2016a, 2016b; Ikari et al. 2009, 2014; Fang et al. 2018; Zhang et al. 2019, 2021; Jia et al. 2022), as well as different sliding velocities and strain rates in the seismic cycles (Beroza and Ide 2011; Ide et al. 2007; Fan et al. 2020). In-situ surveys showed that the fault zones are containing granular abrasive products, i.e., ‘fault gouge’ (Ikari et al. 2009, 2014; Carpenter et al. 2016b; Zhang et al. 2019). The range of gouge layers’ widths can be millimeter-scale up to kilometer-scale (Montgomery and Jones 1992; Unsworth et al. 1997). Natural gouges mostly consist single or groups of phyllosilicate, tectosilicate, and carbonate minerals. Gouge containing tectosilicate minerals (like quartz) often exhibits relatively large shear strength (Blanpied et al. 1995; Zhang et al. 2019). The velocity-weakening behavior in tectosilicate-rich samples is widely detected and dynamic stick–slip events can occur under high normal stress level. On the contrary, phyllosilicate minerals such as talc, illite, chlorite, etc., usually present low frictional strength and have a positive contribution to velocity-strengthening effect causing aseismic slip (Saffer and Marone 2003; Carpenter et al. 2011). For carbonates, which are commonly found in crustal faults, illustrate complex frictional behavior depending on fluids, normal stress levels, sliding velocities, and thermal effects (Verberne et al. 2015; Carpenter et al. 2016b).

It is widely reported that the local movements on preexisting faults, disturbed by both human activities and tectonic effects, results in substantial seismic events (Xu et al. 2016; Foulger et al. 2018; Chen 2020; Harris 2017; Bürgmann 2018; Vlek 2018; Collettini et al. 2019). Mining, explosion, reservoir operation producing variable normal stress affect the natural fault zones, showing a variety of frictional patterns (van der Elst and Savage 2015; Delorey et al. 2017; Beeler et al. 2018; Li et al. 2022). Frictional response of rock fractures under dynamic normal load does not obey the traditional Amontons-Coulomb’s law, showing a unique pattern (e.g., Kilgore et al. 2017; Dang et al. 2021, 2022a, 2022b). These tests revealed how the dynamic loads influence the frictional properties of long-time sliding fractures; however, the frictional properties will also be disturbed during the quasi-stationary contacts.

Faults are known to gain strength after activation, and the activation may then lead to strength loss (Dieterich 1972; Das and Aki 1977). Seismic data revealed that the decrease of tectonic stress in seismic region increases logarithmically with time. Laboratory experiments on rock friction also demonstrated that the friction on static contact (after the yield strength of the friction surface) decreases logarithmically with time (Marone 1998a, 1998b; Marone and Saffer 2015; Im et al. 2017). The stabilities of frictional sliding systems are usually determined by slight variations in friction (induced by velocity or load changes) (Marone 1998a, 1998b; Dieterich and Kilgore 1994; McLaskey et al. 2012). To be specific, direct shear tests were performed using laboratory scale rock fractures (bare or infilled). When the shear stress reaches the yield value, the velocity at the loading point suddenly drops to zero. At this time (‘hold stage’, or ‘relaxation stage’), the shear force still exists, but it will decline rapidly first and then slowly. After, the loading point velocity suddenly returned to its original value, and the laboratory fault would ‘heal’.

This kind of test is referred as ‘slide-hold-slide’ (SHS) (Marone 1998b), which is regarded as a feasible model to simulate seismic cycles in nature. In many researches, SHS tests were performed considering the effects of gouge property, surface geometry, fluids, temperature, etc. (Ikari et al. 2014; Carpenter et al. 2016a, 2016b; Zhang et al. 2019; Fan et al. 2020; Jia et al. 2022). However, in previous researches, SHS tests were carried out under constant normal stress; thus, the role of stress disturbance during fault interseimic periods was little investigated. Therefore, we selected quartz as a representative gouge material to study the fault frictional stability. In this study, we performed one conventional SHS test and two sets of ‘dynamic’ SHS tests to reveal the role of dynamic stress disturbance in the seismic cycles of tectonic faults. The effects of normal load oscillation frequency, normal load oscillation amplitude and normal stress level during the hold stage were explored. This study provides new insights on the frictional behaviors of lithosphere discontinuities and is beneficial for relative disaster prevention of deep mining.

2 Experimental set-up

2.1 Apparatus and samples

All friction experiments were performed in double-direct shear configuration using a self-developed shear apparatus (DWZ-250) (Dang et al. 2022c, Fig. 1a). The test configuration consisted of two identical layers of simulated gouges sandwiched between three granite forcing blocks: a central block and two stationary side blocks (e.g. Marone 1998a; Zhang et al. 2019; Violay et al. 2021). Two hydraulic jacks in horizontal direction were used to apply loads normal to the granite, while a vertical hydraulic jack was used to apply shear load at designed shear rate. Loads were measured using load cells (accuracy ± 0.1 kN), positioned at the end of the ram, which is stiff enough and its self-deformation can be neglected. Horizontal displacements were measured by two LVDTs (linear variable differential transformers) with a resolution of ± 0.1 μm. The load point displacements were measured by a deformation sensor inserted in vertical piston, and the sliding distance was obtained from a vertical LVDT attached on the middle sliding block and its resolution was ± 0.1 μm.

Fig. 1
figure 1

Experimental configuration. a Experimental geometry and loading mode. Red dots are locations where the LVDTs attached b The photo of granite samples and infilled synthetic gouge c The grain size distribution of the quartz powder

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The granite cubes in our experiment were sourced from Chinese Sichuan Province, and previous mechanical test showed its Young’s modulus is 82.8 GPa, the tensile strength is 7.51 MPa, and the uniaxial compressive strength is 151.7 MPa. The sliding surfaces were created with diamond saw and were uniformly polished (Fig. 1b). The length of the central sliding rock and two stationary blocks was 200 mm and 100 mm, respectively. The thickness of every rock sample was 50 mm, and the friction contact area of each side was 0.01 m2. Quartz is the main content of granite which is widely distributed in natural fault zones. A number of previous researches directly used pure quartz powder as the infill material to study the fault mechanics (e.g., Boettcher and Marone 2004; Hong and Marone 2005; Kilgore et al. 2017; Marone and Saffer 2015). We used the commercial-available quartz powder as the simulated fault gouge with the mass of 35 g in each layer, and its purity of SiO2 was no less than 99.5%. Quartz inhibits stick–slip under a relative low stress (Zhang et al. 2019), and stable sliding consistently occurs during the following friction tests. Figure 1c shows its grain size distribution as most particles were between 200 to 700 μm.

2.2 SHS tests

We conducted all the friction experiments in a room-humidity (around 75%) and room-temperature (around 15 °C) environment. These tests were displacement driven (referred by load point position). We consider two common stress levels σn = 5 and 7 MPa. The load point moved after the normal load is gradually applied to 5 MPa. First, we set a constant loading point velocity (vlp) of 0.5 mm/min and a sliding distance of 2 mm for the run-in process (the shear load can reach the steady state). After that, the shear hold was executed at every 0.5 mm load point displacement for 3, 10, 30, 100, 300 and 1000 s during the whole process, and the first hold was started at 2 mm displacement. Next, the normal loading level was gradually increased to 7 MPa, and the previous experiment procedure was repeated. As a result, the final load point displacement was 10 mm.

In the ‘dynamic SHS tests’, the σn oscillated as triangle waves during th. We set different wave amplitudes and frequencies in two test groups (Tests FH1–FH5, Test AH1–AH5) to simulate the dynamic stress disturbance in the fault zone, and the mean normal stress levels did not change. As summarized in Table 1, we conducted a SHS test (Test CH1) under consistent constant normal stress for comparison; Tests FH1–FH5 was concerning the effects of normal load oscillation frequency (f) from 0.1 to 1 Hz, and Test AH1–AH5 was concerning the effects of normal load oscillation amplitude from (ε) 5% to 25%. All the vlp was kept at 0.5 mm/min during slide in this work.

Table 1 Test scheme. All the SHS tests were performed under normal stress level of 5 and 7 MPa
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3 Results and analysis

3.1 General features

Figure 2 reports the shear stress response as a function of load point displacement in the SHS test of the two stress levels. Figure 3 illustrates the important characteristics of the SHS test in this research. As shown in Fig. 3a, when the fault gouge slide to the specified distance, the loading piston stopped moving, and the friction can be observed to decrease continuously (the decreasing rate is fast at first and then slow). After the load point displacement had been maintained for a hold time (th), there was a peak value of friction after the reload, which was mostly higher than the steady-state friction (μss) before the hold. After that, the friction coefficient dropped to reach a new steady-state value, which was similar to the friction before the last hold process. This behavior has been described as ‘Dieterich-type’ friction healing (Chen et al. 2015). Here, two parameters are generally needed to reflect this frictional evolution, namely, ‘friction healing’ and ‘friction relaxation’. In other words, the difference between the μss and the peak friction coefficient after the reload (μpk) is defined as friction healing (Δμw) (Ikari et al. 2014; Carpenter et al. 2016b; Chen et al. 2015). Also, the friction relaxation (Δμc) is calculated by subtracting the minimum friction coefficient during hold (μmin) (usually at the moment before the load point moves again) from the μss. Previous studies have shown that Δμw is controlled by th in a certain range and can be characterized by friction healing rate (βw). As shown in the Eq. (1) and Figs. 4 and 5, if th is marked on a logarithmic x-axis, then Δμw is arranged in a straight line whose slope equals the frictional healing rate. Similarly, as formulated in Eq. (2), the frictional relaxation rate (βc) follows the same logarithmic relation and can be calculated using the same method.

Fig. 2
figure 2

Shear stress evolution of SHS tests. a Test FH1–FH5, σn = 5 MPa b Test FH1–FH5, σn = 7 MPa c Test AH1–AH5, σn = 5 MPa d Test AH1–AH5, σn = 7 MPa

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Fig. 3
figure 3

Anatomy of SHS tests. a A typical SHS result (No. CH1) to derive the frictional healing (Δμw) and frictional relaxation (Δμc) based on the experimental data b Normal stress, load point displacement and shear stress response in a dynamic SHS test c Slip characteristics of fault during holding and the following sliding. δh is the creep length that occurs during the hold, up to the moment when the load point restarts. δp is the onward slip that occurs prior to peak friction, and is referred to as ‘precursory slip’. δs is a measure of the slip necessary from reloading to reach the stable value of sliding friction

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Fig. 4
figure 4

The results of relaxation and frictional healing considering different normal load oscillation frequencies during relaxation stage. a Frictional relaxation for different hold time under normal stress of 5 MPa b Frictional healing for different hold time under normal stress of 5 MPa c Frictional relaxation for different hold time under normal stress of 7 MPa d Frictional healing for different hold time under normal stress of 7 MPa. The results of creep relaxation and frictional healing considering different normal load oscillation amplitudes during relaxation stage e Frictional relaxation for different hold time under normal stress of 5 MPa f Frictional healing for different hold time under normal stress of 5 MPa g Frictional relaxation for different hold time under normal stress of 7 MPa h Frictional healing for different hold time under normal stress of 7 MPa

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Fig. 5
figure 5

The calculated relaxation rate and healing rate under two normal stress levels. a, b Test FH1–FH5 c, d Test AH1–AH5

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Faults can strengthen (heal) between earthquakes, and the rate of this healing process plays a key role in determining earthquake characteristics (Marone 1998b). The overserved Δμw in SHS test is considered the mechanism most likely to be responsible for natural fault strengthening. Higher βw implies that the frictional strength which is necessary to prime fault re-rupture is fast recovered during interseismic period, with an important impact on repeated seismic cycles (Ikari et al. 2014). The frictional relaxation is a consequence of gouge creeping and is analogous to the after-slip in seismic cycles. It is a process to release the strain energy around the fault. As a result, the relaxation Δμc during a certain hold period is associated with earthquake after-slip behavior (Marone et al. 1991; Zhang et al. 2019).

$$\Delta \mu_{{\text{w}}} = \mu_{{{\text{pk}}}} - \mu_{{{\text{ss}}}} = \beta_{{\text{w}}} \cdot \log t_{{\text{h}}}$$
(1)
$$\Delta \mu_{{\text{c}}} = \mu_{{{\text{ss}}}} - \mu_{{{\text{min}}}} = \beta_{{\text{c}}} \cdot \log t_{{\text{h}}}$$
(2)

Moreover, as shown in Fig. 3b, in the tests FH1–FH5 and AH1–AH5 which include oscillatory normal stress during hold stages, in these holds, the fluctuation of normal stress will cause the fluctuation of shear stress, combing with the frictional descending trend similar to the conventional SHS test. For the variation patterns of sliding displacement, Fig. 3c show details of the friction coefficient as a function of two independent measurements of both fault sliding distance (based on the position of middle sliding block) and load point displacement (based on the position of vertical piston) during a 30 s hold (the insert in Fig. 3a). Two friction curves were drawn flowing these two x-axes. Due to finite shear stiffness, "Load point displacement" and "Sliding distance" are not equal. Note that during the hold period, the middle block was not absolutely stationary, but was ‘creeping’ at a low rate. Therefore, when the friction coefficient got its peak value, the corresponding displacements of the sliding block and the load point were not identical. Figure 3c tends to demonstrate slip characteristics of fault during holding and the following sliding. The real sliding velocity of the fault (creep rate) will be discussed in Sect. 4.1, and the δh is the slip (creep length) that occurs during the hold. Additionally, as marked in Fig. 3c, during reload, the μpk cannot be reached immediately, so there is a precursory slip of the load point (δp) prior to peak friction. And we found that the slip length required to reach μss again from the μpk, i.e., δs, is also affected by the normal load oscillations.

3.2 Frictional strengthening and frictional relaxation

Figure 4a–d report the results of frictional relaxation and frictional healing of Test FH1–FH5 (considering different normal load oscillation frequencies during relaxation stage), and Fig. 4e–h report the results of frictional relaxation and frictional healing of Test AH1–AH5 (considering different normal load oscillation amplitudes during relaxation stage). As shown in Fig. 4a–d, compared to the static test, the value of Δμw and Δμc is larger in dynamic tests. However, among these tests, changing the oscillation frequency will not create a remarkable difference of the Δμw and Δμc. As can be seen in Fig. 5a, the values of βc are similar between static and dynamic results, and higher normal stress leads to higher βc for dynamic tests. Besides, the oscillatory normal loads can enhance the magnitude of βw (Fig. 5b), and higher normal stress leads to lower βw for dynamic tests. The oscillation amplitude has an evident influence on Δμw and Δμc. As shown in Fig. 4e–h, compared to the static test, the value of Δμw and Δμc consistently increased in every hold stage, and increasing the oscillation amplitudes will create remarkable enhancement of the Δμw and Δμc among these tests. After the intense normal load oscillation (Test AH4 and AH5), these linear relationships of Δμw or Δμc with log(th) are not perfectly regular. However, the values of βc are still similar between static and dynamic results (Fig. 5c). Also, βw at 5 MPa consistently greater than βw at 7 MPa, and βw increased significantly and uniformly as the amplitude increased (Fig. 5d).

3.3 Frictional response during normal oscillations

As mentioned in Sect. 3.1, in the relaxation stage, the fluctuation of normal force will cause gentle fluctuation of frictional stress. Figure 6a shows the variation pattern of shear stress and apparent friction coefficient (real-time shear stress divided by real-time normal stress) since the beginning of 1000 s hold in the Test AH5. As can be seen, the increase and decrease of shear stress function and normal stress function are consistent, and there is no phase difference between them. This is different from the phenomenon in the stable sliding on fault gouge or bare fractures (Dang et al. 2021, 2022a, 2022b). However, the increase and decrease of the apparent friction coefficient function and the normal stress function are completely opposite, so the phase difference between them always equals half of the period.

Fig. 6
figure 6

The frictional response induced by normal load oscillation during holding stage. a An example of shear stress and apparent friction coefficient variation in the holding stage (1000 s hold) b Variation of friction coefficient (peak to valley) with different oscillation frequencies and amplitudes c The shear loading rate as a function of normal loading rate d The shear load response sensitivity (shear loading rate divided by normal loading rate) as a function of normal loading rate

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Figure 6b reports the variation of friction coefficient (peak to valley) with different oscillation frequencies and amplitudes. Varying the oscillation frequency of normal load does not change the variation magnitude of apparent friction coefficient. However, the variation of the apparent friction coefficient in a cycle is proportional to the amplitude of the oscillatory normal load. We also calculated the shear loading rate as a function of normal loading rate. As shown in Fig. 6c, the shear loading rate is also proportional to the normal loading rate, and both increase synchronously in the two groups of experiments. However, as shown in Fig. 6d, the corresponding variation proportion is weak, with only around 4.5% of the magnitude of the normal effect.

3.4 Normal deformation

The dilation or compaction normal to the sliding plane also play an important role in the seismic cycles combining with the relaxation and strengthening processes (Marone 1998b; Ikari et al. 2009; Marone and Saffer 2015; Carpenter et al. 2016b; Zhang et al. 2019). Because of the much greater Young’s modulus of the granite matrix, almost normal deformation during the test originated from the infilled gouge. We analyzed the normal deformation patterns (total deformation concluding two layers) of the gouge layer when σn = 5 MPa, and reported the results in Fig. 7. In all the tests, continuous shearing resulted in significant compaction and it contributed to the increase of shear stress. In addition to the compaction due to the shear motion, some part of compaction of the layer was also obtained during static contact (shown in Fig. 7). In the SHS test, the layer is always compacted during the hold, and existing works showed that layer compaction proceeds roughly linearly with log hold time in SHS tests (Marone and Saffer 2015; Carpenter et al. 2016b).

Fig. 7
figure 7

Normal deformation of the whole shear process when σn = 5 MPa. a Test FH1–FH5 b Test AH1–AH5

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In this work, we focus on the normal deformation variation that happened in the hold period. As shown in Fig. 8a, under the oscillatory normal load, the gouge layers were compressed and released periodically, so the normal displacement curves also follow the term of triangular wave. The normal displacement variation during one load cycle (Δud) remains basically unchanged, and there is no phase lag between the normal stress and the normal displacement. Moreover, the change of layer thickness can be considered as a restorable deformation in a short time span, so the normal stiffness of the layer can be calculated as Δud/2A. As shown in Fig. 8b, Δud does not experience a significant change when normal load oscillation frequency varies; in Fig. 8c, Δud increases linearly with the increase of oscillation amplitude. So the normal stiffness of the quartz layer nearly keeps a constant of around 160 MPa/mm under different loading conditions.

Fig. 8
figure 8

a Normal displacement variation effected by oscillatory normal load in hold stage; the characteristics of cyclic normal deformation considering b Normal load oscillation frequency and c Oscillation amplitude, which includes the normal deformation in a load cycle during 300 s hold under the normal load of 5 MPa and the calculated normal stiffness

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4 Discussion

4.1 Creep and precursory slip

Figures 9 and 10 present the slip characteristics (creep during the hold and the precursory slip δp after reload) under two stress levels. The slip patterns under 5 and 7 MPa normal stresses are similar. During the hold stage, the sliding surfaces were still creeping at a very low rate although the loading point was stationary. As shown in Fig. 9a, c, for different normal load oscillation frequencies, the creep rate decreases with the increase of holding time, and the logarithm of the two variables shows nearly linear relations in the plots. Also, there is no obvious distinction between the static and the dynamic tests. As shown in Fig. 10a, c, for different oscillation amplitudes, the creep patterns are similar, and the difference between the static and dynamic tests are also not obvious. The precursory slip is an essential parameter in fault friction (Johnson 1981; Acosta et al. 2019; Cattania and Segall 2021). Similarly, the effect of normal stress level is minor. As shown in Fig. 9b, d, the δp can also scale with hold time by a logarithmic linear relationship. However, this linear trend cannot be kept when the oscillation amplitude is large (Fig. 10b, d). From the two sets of dynamic tests, we can see that the oscillatory normal load will increase the magnitude of δp. Meanwhile, the δp consistently increases when the normalized oscillation amplitude is larger, but δp does not shown much difference when adjusting normal load oscillation frequency.

Fig. 9
figure 9

Details of relaxation creep rate and precursory slip length in SHS tests considering different normal load oscillation frequencies during relaxation stage. a Creep rate for different hold time under normal stress of 5 MPa b Precursory slip length for different hold time under normal stress of 5 MPa c Creep rate for different hold time under normal stress of 7 MPa d Precursory slip length for different hold time under normal stress of 7 MPa

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Fig. 10
figure 10

Details of relaxation creep rate and precursory slip length in SHS tests considering different normal load oscillation amplitudes during relaxation stage. a Creep rate for different hold time under normal stress of 5 MPa b Precursory slip length for different hold time under normal stress of 5 MPa c Creep rate for different hold time under normal stress of 7 MPa d Precursory slip length for different hold time under normal stress of 7 MPa

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4.2 Delayed steady state

As can be seen in Fig. 3, the evolution of after-peak friction coefficient shows a decrease until it reaches the μss again. The residual slip (δs) in Fig. 3c is the slip necessary to reestablish steady sliding, i.e., the slip at which friction-displacement curves become flat again. Previous researches reported the δs seems to scale with hold time, too (Marone and Saffer 2015). As shown in Fig. 11, we found that compared to conventional SHS tests, the average descending rates of friction coefficient (the main slope of the friction curves after peak) are much lower, causing that the return to frictional steady state is delayed (the δs will be longer). As shown in Fig. 11a, the descending rates do not experience an obvious change when the frequency of oscillatory normal load during hold increases. However, as shown in Fig. 11b, by improving the oscillation amplitude, the rate of friction decreasing reduces consistently, causing a longer distance to reach μss.

Fig. 11
figure 11

The post-peak slope (the rate of friction descending) which demonstrates the delayed steady state as a function of a Normal load oscillation frequency and b Normalized normal load oscillation amplitude

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When explaining the larger Δμw, Δμc and friction descending rate in the dynamic tests, this result is potentially caused by the rearrangement of the gouge particles owning to the oscillatory normal stress. Generally, frictional healing is the process that the faults regain the shear strength through the increase of micro-contact area (Ikari et al. 2014). During last hold, the crushed mineral particles bond together through the normal compression and the number particle–particle contact points increased (Jia et al. 2022). As the normal deformation increases linearly with the increase of ε (Fig. 8), consequently, larger ε causes larger Δμw. However, the normal deformation does not experience a significant change when f varies, indicating that changing the f will not create a remarkable difference of the Δμw. Similarly, the gouge was more strengthened through the increase of micro-contact area because of oscillatory σn in hold period, causing the longer δs. And f has a minor effect because the micro-contact condition is stable with same oscillation amplitude. As for frictional relaxation, the hold periods are processes to release the strain energy stored in the shear system and cause shear load reductions (Marone 1991). The energy is faster released when normal load is more dramatically unloaded, hence larger ε causing larger Δμc.

5 Conclusions

To explore the effects of varied normal load on the fault friction during interseismic period, dynamic slide-hold-slide (SHS) tests on quartz gouge were performed. We used oscillatory normal stress considering different normal load oscillation frequency and amplitude during the quasi-stationary contact (hold) process.

During hold stages, the fluctuation of normal stress will cause the fluctuation of shear stress, combing with the frictional descending trend similar to the conventional SHS test. The normal load oscillation amplitude can make a positive effect on the relaxation and healing characteristics. Both the magnitude of frictional relaxation and frictional healing consistently increase with larger oscillation amplitude, and the rate of frictional healing increases uniformly when improving the oscillation amplitude. But the frictional relaxation rate is not notably affected by the oscillation amplitude under two stress levels. All of these characteristics do not experience an obvious evolution when changing the normal load oscillation frequency. Besides, during the process of relaxation, the shear stress fluctuates synchronously with the normal stress, the shear loading rate is proportional to the normal loading rate, and the normal stiffness of the quartz layer nearly keeps a constant under different normal loading conditions. During the hold stage, the sliding surfaces are still creeping at a very low rate, which shows no obvious distinction between the static test and the dynamic tests. The precursory slip also scales with hold time by a logarithmic linear relationship, and it is increased by larger oscillation amplitude. Compared to conventional SHS tests, the descending rates of friction coefficient in the dynamic tests are much lower, causing the delayed return to frictional steady state.

In the current study, the mineral contents and initial thickness of gouge kept the same, so these factors will be studied in the future. Besides, we will upgrade our apparatus with dual syringe pumps so that the dynamic hydraulic effects (Ji et al. 2022; Ma et al. 2022) on faults healing will be explored.