1 Introduction

The tectonic faults and fractures dominate the stability of rock mass, and the frictional sliding phenomena of these discontinuities with long or short timespans are widely detected (Harris 2017; Bürgmann 2018). Stick–slip and stable sliding are the two types of slip behaviors of a pre-existing fault. Thus, in the past decades, a number of laboratory investigations on shear behavior of rock fractures (including stable sliding process and stick–slip rupture) were performed, of which results revealed the effects of constant normal stress or stiffness (Meng et al. 2018; Bista et al. 2020; Liu et al. 2020; Zhou et al. 2021; Zhang et al. 2022), and surface roughness (Badt et al. 2016; Sagy and Lyakhovsky 2019; Fan et al. 2018; Wang et al. 2020; Morad et al. 2022). Also, some shear strength criterions were built based on experimental observations and have been used in practice (Prassetyo et al. 2017; Bista et al. 2020; Li et al. 2020; Liu et al. 2020).

The convincible link between rock stick-slips and earthquakes was first revealed by Brace and Byerlee (1966). Since most tectonic seismicity is caused by the sudden release of elastic strain energy when faults slip, stick–slip is the basic mechanism of the nucleation of shallow earthquakes (Noda and Lapusta 2013; Dorostkar and Carmeliet 2018; Zhou et al. 2021; Passarelli et al. 2021). The mechanics of a spring-block connection model suggests that stick–slip occurs when the elastic stiffness of the surrounding shear system is less than a critical stiffness, whereas stable sliding appears when loaded by stiffer springs (Ruina 1983; Rice and Ruina 1983). This critical stiffness depends on effective normal stress and other physical properties described in the well-known rate and state (RS) friction law (Dieterich 1979; Ruina 1983; Marone 1998). Recently, laboratory stick–slip experiment has been fully considered as an effective way to explore the mechanism of earthquake nucleation, accompanied by high-precision measurement technology, such as photoelastic technology, acoustic emission detection, etc. (Selvadurai and Glaser 2015; Mclaskey and Yamashita 2017; Wu et al. 2021; Cebry et al. 2022). The slip mode varies systematically as a function of the critical stiffness ratio, and the slow-slip events or period-multiplying in the stick–slip cycles can be observed by reducing applied normal stress (Leeman et al 2016, 2018; Mei et al. 2021, 2022).

The in-situ stress around fault zones never maintains constant (Chen 2020; Shen et al. 2023). Natural effects such as tides, glacier movement, co-seismic effects, and human works such as underground explosions, mining, and fluid injection can cause great disturbance to the stress condition of the fault zones (Cao et al. 2016; Delorey et al. 2017; Noël et al. 2019; Ji et al. 2022). The stable sliding characteristics of rock fracture under changing normal stress are thoroughly studied in previous researches (Boettcher and Marone 2004; Dang et al. 2021, 2022a; Dang and Konietzky 2022; Kilgore et al. 2017; Tao et al. 2023; Tao and Dang 2023). However, when the fractures undergo slip instabilities (frictional ruptures), how the cyclic normal stress influences the slip style is poorly known. Here, we declare the nomenclature that the ‘slick–slip’ is only used when the normal stress is a constant. When the form of normal stress is cyclic, the frictional ruptures are plainly expressed as ‘fast slip’ or ‘slip events’.

In this study, we explore the systematic changes of rock dynamic friction patterns as a function of amplitudes of cyclic normal stress. We first present the shear stress response of a planar granite fracture under both constant normal stress and varied normal stress with oscillation amplitude ranging from 10% to 70%. The shear strength, recurrence, slip patterns are analyzed in the following sections. Moreover, effective frictional parameters derived from RS friction law are introduced to explain the evolution patterns of fast slip events. This work deepens our understanding of rupture dynamics of rock discontinuities and is beneficial for relative geohazards mitigations.

2 Experimental set-up

We performed all the shear tests on granite samples using a self-developed shear box device, DJZ-500 (Dang et al. 2022b). As shown in Fig. 1a a granite cubic sample was cut into the same two half pieces, each half block with a size of length × width × height = 100mm × 100mm × 50  mm. The upper shear box was fixed and the lower shear box moved monotonically. A horizontal LVDT measured the shear displacement of the shear box. Four vertical LVDTs measured the dilatancy of the upper block during shear. The horizontal load piston was displacement-driven to provide a designed load point velocity (vlp), and the vertical piston was force-driven which executed constant or cyclic load signals. All the forces and displacements were recorded 50 times per second with accuracies of 0.1 kN and 0.1 μm, respectively.

Fig. 1
figure 1

Shear box apparatus and the experimental material. a The loading assembly of DJZ-500. The fractured granite sample was installed in the shear box with the size of length × width = 100mm × 100 mm. The upper shear box is fixed and the lower shear box moves monotonically b The saw-cut granite pieces in the tests c Microscopic image of the granite showing the main mineral compositions; Pl: plagioclase, Qtz: quartz, Bt: biotite, Kfs: K-feldspar d The topographic map of the saw-cut surface e Four profiles of the scanned surface along shear direction

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As shown in Fig. 1b and c, we used two saw-cut granite blocks soured from Hengyang, China. The nominal contact area during shear is 0.01 m2. The uniaxial compress test reported its Young’s modulus is 83 GPa. At first, the sliding surface were carefully polished by fine sandpapers. In order to generate stable and repeatable stick–slip events under constant normal stress, the finely smoothed fracture was preliminarily sheared under 5 MPa normal stress for several times until the frictional response presented unchangeable stick–slip behavior which owned constant stress drop and friction strength.

After this, the surface topography was scanned by the X-TOM optical scanning system with a resolution of 1 μm. The scanned data are drawn in Fig. 1d. As shown in Fig. 1e, the roughness is evaluated by the root mean square heights (RMS) of the asperities. The RMS of one profile can be calculated by Eq. (1).

$$\text{RMS}_{X} { = }\left[ {\frac{1}{L}\int\limits_{0}^{L} {Z^{2} {\text{d}}Y} } \right]^{1/2}$$
(1)

where, Z is the height of the scanned point; Y is the distance along the shear direction; L is the total profile length. In the investigation from Morad et al. (2022), stick–slip phenomenon can be observed when the RMS is 1–50 μm. In our work, the four profiles (with coordinates perpendicular to shear direction X = 5, 35, 65 and 95 mm) shown in Fig. 1e have similar RMS value of around 30 μm.

The box sheared the fracture loaded by a constant vlp of 1 mm/min. In the first 2.0 mm load point displacement, the vertical piston offered a constant load of 50 kN (i.e. 5.0 MPa for average stress). During the sliding process from 2.0 to 5.0 mm load point displacement, the normal stress (σn) varied periodically in a triangular way with a frequency f = 0.2 Hz. After that, σn returns to its constant origin value. As shown in Table 1, tests PA1–PA5 consider the effect of increasing normal stress oscillation amplitude (A) from 0.5 to 3.5 MPa (i.e., normalized amplitude A* from 0.1 to 0.7).

Table 1 Experiments performed in this study. The fracture was sliding with a constant velocity subjected to constant and periodic normal stress
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3 Results and analysis

3.1 Shear stress response

We analyze the shear stress (τ) variation as a function of load point displacement. As shown in Fig. 2, for the frictional patterns in the initial 2.0 mm (shear under constant normal stress conditions), the characteristics of stick–slip cycles under constant normal stress are nearly identical in Test PA1–PA5, which also confirms the repeatability in our study. To be specific, the stress drop of each slip is around 1.05 MPa, and the recurrence timespan is about 5 s (0.08 mm load point displacement). When the load point reaches 2.0 mm distance, the normal stress becomes oscillatory; the shear stress curves experience a transition which is dependent on the load oscillation amplitudes. In Figs. 2a and b, when the disturbance is relatively small (A* < 0.2), the fast slip events show chaotic shapes. The shear stress drop and recurrence time cannot keep stable, and the peak/valley values of shear stress also fluctuate. However, as can be observed in Figs. 2d and e, the slip styles can be regular when the disturbance is large enough (A* > 0.6). In the tests PA4 and PA5, under cyclic normal stress, the slip ruptures show compound style, that is, the sudden slip of shear fracture with faster velocity and smaller velocity occurs alternately, and the extremums of shear stress curves keep nearly unchanged with increasing load point displacement. Also, the period of each slip event pair approximately equals the normal stress oscillation period. In all tests, when the normal stress variation stops (at 5.0 mm displacement), the shear stress will return to the initial form so the frictional response is recoverable.

Fig. 2
figure 2

Shear stress as a function of sliding distance under constant and cyclic loading condition of bare fractures. a Test PA1 b Test PA2 c Test PA3 d Test PA4 e Test PA5

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We use the random walks (Lockner and Beeler 1999; Noël et al. 2019) to explore whether the phase of σn functions can decide the activations of fast slip events. The mid-value point of σn is defined as the phase of zero, so the peak point corresponds to the phase angle of 90° and the valley was 270° (or − 90°). As formulated in Eq. (2), the possibility of ending a random walk (Prw) is a function of events number (N) and the walked distance from the start point (D) (Schuster 1897). As shown in Fig. 3, as all the curves walking out of the corresponding circles, the hypothesis that sequences of events are random (uncorrelated with the forcing function) can be rejected at the 99.5% confidence level. The phase angles at the end of the random walks (φe) indicating the dominant timing of activation are also marked in Fig. 3; clearly, all the φe are in the zone of unloading (the two and third quadrant). The smaller the amplitude of normal force disturbance is, the earlier the φe exists. The larger the A*, the straighter the random walk path, which means the occurrence fast slip events tends to be more predictable and organized. When A* = 0.7 (Fig. 2e), the slip style is always that big and small slip events appear in succession, so the random walk path (red line) is a regular double fold line.

$$P_{{\text{rw}}} {\text{ = e}}^{{ - D^{2} /N}}$$
(2)
Fig. 3
figure 3

Random walks of fast slip events happened under cyclic normal stress. The east direction is the zero phase of normal stress. All the random walks exceed critical distance and have high probabilities (> 99.5%) of being correlated with the σn oscillations; the phases at the end of the random walks (φe) are noted

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3.2 Shear strength weakening

The regular stick–slip cycles happened under constant normal stress in test PA1–PA5 have nearly identical peak, valley and mean strengths (the pre-oscillation shear strengths, τpreP, τpreV, τpreM) of around 2.24, 1.09 and 1.67 MPa, respectively. As shown in Fig. 4, the frictional strength under cyclic normal stress (the disturbed shear strength, τdP, τdV, τdM) is changed. As illustrated in Fig. 4b, all the shear strengths are decreasing with larger A*. When A* excesses 0.2, the τdP will be smaller than τpreP. Compared to former studies on stable sliding process of rock fracture (Dang et al. 2021, 2022a), the dynamic weakening phenomenon happens under relatively larger normalized oscillation amplitudes (55%–90%). However, if the fractures experienced the stick–slip cycles, the normal oscillation is much easier to induce the frictional weakening. Furthermore, τdV, τdM are consistently weakened compared to pre-oscillation occasions in all the tests. When A* = 0.7, τdP, τdV and τdM are weakened by 46%, 67% and 53% compared to τpreP, τpreV, τpreM, respectively. Taking test PA5 for example, just after the transition moment of normal stress shape, several shear stress drops occurred (the blue line in Fig. 4a), resulting in that the shear stress fluctuates at a lower level, which is recoverable after ending the normal stress oscillation. Moreover, the range of shear stress during rupture cycles (τdP–τdV) is narrowing when enhancing the normal oscillation amplitude.

Fig. 4
figure 4

Charecteristics of shear strength. a The observed cyclic normal stress induced shear strength weakening characterized by peak, valley and mean shear stress in the slip cycles. b The peak, valley and mean value of shear stress under periodic normal stress as a function of normalized oscillation amplitude

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3.3 Recurrence of slip events

Figure 5 shows the transitions of recurrence pattern and stress drop of slip rupture cycles from constant normal stress condition to cyclic normal stress condition. The stress drops are collected from the events shown in the right column of Fig. 2. We use the distance that the load point had gone to represent the timespans between the slip events. The inclined dash lines indicate the timespan ratio from pre-event to post-event, so the regular stick–slip events that occurred under unchangeable normal stress are located near the 1/1 ratio line, i.e., the interval of each slip is similar (Veedu and Barbot 2016). In Figs. 5a and b, when A* < 0.2, the events shifting routes are not predictable enough which are mostly located in the 1/2– 2/1 interval range, and the shear stress drops are not obviously reduced under cyclic normal stress. As the amplitude increasing, the range of pre-event to post-event timespan ratio becomes wider and more predictable. In the tests PA4 and PA5 (Figs. 5d, e), when the normal stress oscillation begins, after 3–4 events, the recurrence patterns become stable which sways in the range of 8/1 to 1/8 time ratio. Also, the shear stress drops are obviously relieved and stabilized into two levels. In other words, the continuous normal loading–unloading process with large amplitude let the shear stress drop in once slip event cannot be released singly.

Fig. 5
figure 5

Recurrence pattern and shear stress drop of slick–slip events in the a Test PA1, b Test PA2, c Test PA3, d Test PA4 and e Test PA5. Magnitude of stress drop in each event is shown by the color bar. ‘★’ indicates the moment when normal stress oscillation began

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The slip movements are also characterized by variable length and velocity in every slip events. Among the stick–slip events under constant normal stress (Fig. 6a), the slip velocities are between 0.6–1.0 mm/s, which are faster than most of slow slip events in nature (< 10–4 m/s) but slower than general seismic ruptures (> 10–2 m/s) (Tinti et al. 2016). The calculated velocities are similar with former laboratory investigations (Mei et al. 2021; Morad et al. 2022). The slip lengths of every event are also close as the shear box twitches for around 20–25 μm recorded by the horizontal LVDT. The slip deficit is defined as the difference between the load point displacement (δlp, i.e., vlp × t) and the real sliding distance of the shear box. In Fig. 6a, the deficit variation is regular under constant normal stress, as the sudden decrease after slip is similar and the slopes during the stick stages are nearly identical. As shown in Figs. 6b–d, the time series of slip length and velocity showing much disorganized appearances when A* is smaller than 0.4. Each slip takes over about 10–20 μm length, and the maximum velocity decreases with larger amplitude. However, the slip patterns will return to be very structured if A* reaches 0.6 (Figs. 6e, f), as the slip length oscillating back and forth between 15 and 7.5 μm, characterized by alternate velocities which in the range of 0.1–0.8 mm/s. In these cases, the slip deficits also become regular, and the stick slopes before the small slips is much sharper than big ones in the rupture cycles.

Fig. 6
figure 6

Slip deficit, slip length with the slip velocity shown by the color bar during dynamic ruptures as functions of 30 s experimental time under a Unchangeable normal stress and oscillatory normal stress with b 0.1, c 0.2, d 0.4, e 0.6 and f 0.7 normalized amplitudes

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3.4 Apparent friction coefficient

We calculated the apparent friction coefficient (μ = τ /σn) in the tests, where σn and τ are real-time normal stress and real-time shear stress during the frictional sliding. Figure 7 shows the apparent friction coefficient versus load point displacement for different A*. Yellow bars refer to the moment when normal stress oscillation begins. In the initial stick–slip cycles, the friction coefficient after the fast-slip moment is called ‘residual friction strength’ (μr). Under constant normal stress, μr = 0.22. When the normal disturbances are small, as shown in Figs. 7a and b, the variation pattern of μ is chaotic because of the irregular shapes of shear stress (Figs. 2a, b). Also, the minimum μ is never smaller than μr. This reveals that the cyclic normal stress has limited impact on the frictional response. However, when increasing the A*, μ can also become a periodic function of load point displacement. As shown in Figs. 7c–e, the apparent friction coefficient fluctuates intensively when fast slip occurs. The valley value of μ is always corresponds to the peak value of σn. As summarized in Fig. 7f, the valley value of μ decreases with larger A*, being irrelevant to the residual friction strength. The peak value of μ during the cycles are similar for different, which is smaller than the peak value in the pre-oscillation stage.

Fig. 7
figure 7

Apparent friction coefficient as a function of load point displacement under constant and cyclic loading condition. a Test PA1, b Test PA2, c Test PA3, d Test PA4 and e Test PA5. Yellow bars refer to the moment when normal stress oscillation begins. f The peak and valley values of the friction coefficient are presented

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The friction data reveal that the oscillatory normal stress immensely disturbs the fracture frictional rupture behaviors from the regular form to a compound way. The reoccurrence of the slip events is completely related to the normal stress oscillation phase when the disturbance is large enough. Here, we use Coulomb failure function (ΔCFF) to evaluate the frictional tolerance in the rupture process. ΔCFF is defined as changes of Coulomb failure stress, i.e., ΔCFF = Δτ − μr Δσn (here pore pressure change is not considered). Positive ΔCFF indicates that the fault moves closer to failure; whereas a negative ΔCFF indicates that the fault is remaining stable (Lockner and Beeler 1999; Hager et al. 2021). If we set the reference point as the residual stress state, i.e., Δτ = τ − τr. and τ = μσn, the ΔCFF is a function of apparent friction coefficient and rea-time normal stress (Eq. (3)), so it can be regarded as another expression of the changeable apparent friction coefficient.

$$\Delta \text{CFF} = (\mu - \mu_{{\text{r}}} )\sigma_{{\text{n}}}$$
(3)

Figures 8a–e show the variation of ΔCFF as a function of load point displacement within the same scopes in Fig. 7 which including responses under both constant and cyclic σn. We also plotted normal stress curves in the backgrounds for reference. From Eq. (3), ΔCFF and τ curves have identical shapes under constant σn. The grey area corresponds the negative ΔCFF value, and in the regular stick–slip cycles under constant normal stress, it fluctuates beyond the separation line which indicates the residual friction strength. If A* is no more than 0.2, all the ΔCFF > 0, the function curves always return to the zero level after fast slips, similar to the regular events before, but the curve shapes changed compared to the pre-oscillation stage because of the changeable σn. However, the large oscillation amplitudes can reduce the ΔCFF. When A* is 0.4–0.7, all the minimum values of ΔCFF are less than zero and it decreases with larger A*. As shown in Fig. 8f, the maximum ΔCFF during normal stress oscillation (the tolerance of extra coulomb friction) decreases with larger oscillation amplitudes, which means the slip events are easier to be triggered with the normal disturbance, resulting in more events number and greater risks of seismicity. However, the magnitude and intensity of these ruptures is lowered, and the ΔCFF also returns to zero after the first slip if the rupture style is compound (A* = 0.6 and 0.7). Moreover, ΔCFF linearly decreased in the loading stages when the normalized amplitude is larger than 0.4 (Figs. 8c–e), hence inhibiting the activation of slip ruptures.

Fig. 8
figure 8

The variation of Coulomb failure function (ΔCFF) with and without cyclic normal stress in the a Test PA1, b Test PA2, c Test PA3, d Test PA4 and e Test PA5. The grey areas indicate the negative ΔCFF where sliding instabilities cannot happen

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3.5 Normal deformation

Here, we analyze the displacement response in the normal direction which is affected by both the rupture cycles and the normal stress patterns. As the rock matrix has very high Young’s modulus, the normal displacement variation is almost constituted by the deformation of the sliding fracture. In Fig. 9, the positive value means the downward displacement, and we present recorded data points rather than draw the curves to avoid the misguidance of the sensor noise. Clearly, among tests PA1–PA5, the fracture is mostly compressed during shear (Fig. 9a), and before the first 2 mm load point displacement, the compaction of the fracture is about 30–35 μm. The zoom-in (Fig. 9b) shows that the normal displacement also changes periodically under oscillatory normal stress. The variation of normal displacement in one load cycle consistently increases with larger A*; when A* = 0.7, the normal displacement can even reach the negative value, which means the fracture can be gently dilated by the intensive normal unloading.

Fig. 9
figure 9

Normal displacement variation during the shear process. a The normal displacement as a function of load point displacement from 1 to 6 mm in the Test PA1–PA5 b Zoom-in of the upper plot; and the correlated evolution between the shear stress and normal displacement under c constant or d cyclic normal stress

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As shown in Fig. 9c, the normal deformation of the fracture also interfered by the stick–slip cycles. The green points reflect the normal displacement in test PA5, combined with the stick–slip curve of the shear stress. It can be seen that the normal displacement fluctuates within a range of less than 2 μm and has the same period with the shear stress. The normal displacement reaches the peak in the stick stage and then drop to valley during the fast slip. According to study of Morad et al. (2022), it reveals the overriding of micro asperities that the normal displacement variations and stick–slip ruptures being completely in phase. Asperities overriding usually happens on the smooth fractures, while the rough surfaces show the ‘shearing through’ mechanism as the normal compaction consistently increases. Little gouge being observed in our tests also confirmed this assumption. However, as shown in Fig. 9d, under varied normal stress, the normal displacement is mainly dominated by the loading/unloading process.

4 Discussion

As mentioned in the introduction, the shear stiffness highly controls the frictional stabilities; if the loading stiffness of the shear assembly smaller than a critical value (k < kc), the stable sliding cannot maintain. The critical stiffness which derived from RS friction law is calculated as kc = (b − a) σn/Dc (Ruina 1983), which is a proportional function of the real-time normal stress. Based on RS friction theory, as shown in Eq. (4) and Fig. 10a, the scales of (b – a) is dependent by the friction coefficient variation under constant normal load as a result of sudden shear loading velocity change (μ1 to μ2 induced by v1 to v2) (Marone 1998).

Fig. 10
figure 10

a Frictional coefficient variation in VS test to derive RS friction parameters. b A VS test to obtain the (b − a) value. c The decrease of Dieterich-Ruina-Rice number during normal unloading

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Shown in Fig. 10b is the result of a velocity stepping test performed under relatively low constant σn = 1.0 MPa to avoid stick–slip. It confirms that the friction coefficient deceases with larger velocity (velocity wakening behavior). Using the algorithm proposed by Skarbek and Savage (2019), positive (b – a) value is calculated as 0.004, and the parameter Dc is calculated as 11 μm. Hence, to vary the critical stiffness, imposing different normal stresses is an effective way to create a wide range of slip behaviors (Mei et al. 2021, 2022). Besides, as shown in Eq. (5), we estimate the effective stiffness of the sliding system in the stick–slip cycles under constant normal stress (k = 220.66 MPa/m) from the slope of the linear loading curve (Leeman et al. 2016, 2018; Mei et al. 2021). Here, we introduce a non-dimensional parameter, Dieterich-Ruina-Rice number (Ru = kc/k, the stiffness ratio, formulated in Eq. (6)), which is proportional to critical stiffness if the loading stiffness keeping constant. Therefore, Ru linearly changed with the linearly varied normal stress in our tests. Former studies point out small Ru leads to milder frictional rupture as less elastic energy can be stored in the stick stages (Leeman et al. 2018; Scuderi et al. 2020; Mei et al. 2022).

$$\mu_{2} - \mu_{1} { = (}b{ - }a{)}\ln \left( {\frac{{v_{2} }}{{v_{1} }}} \right)$$
(4)
$$\frac{{{\text{d}}\tau }}{{{\text{d}}t}} = k\left( {v_{{{\text{lp}}}} - v} \right)$$
(5)
$$R_{{\text{u}}} = \frac{{k_{{\text{c}}} }}{k} = \frac{1}{k}\frac{{(b - a)\sigma_{{\text{n}}} }}{{D_{{\text{c}}} }}$$
(6)

As almost the fast slip events happen during the normal unloading stage, we plot Ru versus the unloading timespan for different normalized amplitude (same as unloading rate), i.e., the straight lines with deferent slopes in Fig. 10c. The colored arrow-marks correspond the moments when instabilities occur. In test PA4 and PA5, the fast slip events happen more than once during the 2.5 s unloading in a load cycle (Fig. 6); the first events own a faster velocity, longer slip length and greater stress drop while the following event has a mild scale. So the marks (red and blue ones) are separated with different width in Fig. 10c. This explains the compound rupture styles under large cyclic normal stress amplitude. As the first event is activated by the fast growing ΔCFF, but the Ru number sharply decreases at the same time. A smaller Ru mitigates the intensity of the rupture, making big and small events appear in succession.

The compound slip appearances that slow and fast slip events occur alternatively in laboratory are similar to ‘period multiplying’-type instabilities in tectonic faults which are also combined with the compound style (Veedu and Barbot 2016; Veedu et al. 2020; Mei et al. 2021), such as the periodic doubling tremors happened in San Andreas Fault, California (Veedu et al. 2020). As the frictional ruptures are sometimes showing period-multiplying in many natural faults, we believe the periodic local stress disturbance have a strong relation with these observed slip bifurcations (Veedu et al. 2020). This kind of bifurcations were previously studied through the shear tests with normal step unloading. In this work, we found the cyclic normal stress with intensive variation amplitude can also causing the alternate emergence of stress drop and slip velocity. The observed complex sequences of slow and fast stick -slips experimentally provide a link between the swift local stress drops and failure mode of natural faults. It helps to explain why some faults do not appear to fail in a single mode, displaying both slow and fast rupture (e.g., Mw 9.0 Tohoku-Oki earthquake, Mw 8.2 Iquique earthquake) (Veedu et al. 2020).

Indeed, this laboratory study still has limitations. It is hard to observe repeatable and stable seismic radiations from fault zones in nature, as the ruptures are always under the control of roughness, fluid, temperature, and stress disturbance. Although the rupture cycles of faults can be adjusted by long-term effect like tides (lower than 10–3 Hz) (Delorey et al. 2017) or sudden perturbations such as passing seismic waves (up to 10 Hz) from other distant earthquakes (Hatakeyama et al. 2017), the role of oscillation frequencies is rarely acknowledged. During the long-term evolution of seismogenic faults, tectonic movement rates (e.g., shear loading rate) in the local regions is also constantly changing (Scuderi et al. 2016; Leeman et al 2018). Since the shear rate of the sliding system affects another essential friction parameter, Rb = b/(b – a), previous research confirmed that a low velocity promotes the slip transition and enhances the stress drop and AE energy (Mei et al. 2022). Bedsides, compared to bare fractures, the frictional behavior of infilled fractures relating to gouge properties (Lyu et al. 2019; Okamoto et al. 2020) and underground water (Ma et al. 2022, 2023) also needs exploration. Investigations considering these factors and further applications in the natural fault zooms will be conducted in the future.

5 Conclusions

This paper explores the frictional response of a saw-cut fracture imposed by constant shear velocity under a varied normal stress characterized by different variation magnitudes in laboratory. We found that the normal stress oscillation amplitude and the periodic loading function phase guide the styles of slip movement. The experiments documented the rupture style transitions from regular stick–slip to chaotic slip, and eventually to compound slip style.

Laboratory observations reveal that all the slip events are happened during normal unloading, and there is a statistical correlation between the onsets of slip events and the phase of normal stress cyclic function. The triggering of fast slip events shall be delayed with larger amplitude of cyclic normal stress combined with more predictable timing. The frictional strength is weakened by the cyclic normal stress and the weakening effect is greater than the occasions without slip ruptures, and the stress drops are relieved by the larger oscillation impact. The recurrence pattern of slip ruptures is characterized by a ratio between the timespan since previous event and the timespan to next event, and increasing the oscillation amplitude widens the range of the interval ratio. The rupture can transfer to a compound style under larger amplitudes which shows similarities with period-doubling tremors in the tectonic fault zooms. Moreover, the normal displacement displays periodic shapes under both constant and cyclic normal stress affected by both asperities overriding and normal stress variation. The mechanism behind the rupture transitions is related to the inclining rate of stiffness ratio during normal unloading.