The sandstone used in these experiments is a typical rock from the earthquake-prone Longmenshan Fault Zone of the Sichuan Basin, China (Wang et al., 2014; Long et al., 2022). To ensure the samples had comparable structural properties, cylindrical sandstone samples were cored from individual sandstone blocks along a direction perpendicular to the laminae. The ends of each cylindrical rock sample were carefully ground to a height of 100 mm and a diameter of 50 mm.

The complete sandstone samples were sawed from the center at angles of 0°, 15°, 30°, 35°, 40°, 45°, 50°, 55°, 60°, and 65° relative to the direction of σ 3 (Figure 1B). The saw-cut surface was polished using 320-grit sandpaper to ensure uniform surface roughness. The gypsum fault was created by mixing 10 μ m bassanite powder with water in a 3:1 ratio, then filling the mixture into the saw-cut surface. The saw-cut surface was then compacted to ensure the gypsum layer thickness was 2 mm. After the bassanite powder rehydrates, it re-bonds the saw-cut surfaces. The specimen was left undisturbed under room temperature and atmospheric pressure for 2 days. The end surfaces of the samples were then checked for flatness. If the maximum height difference were less than 0.05 mm (Cvitanovic et al., 2015), the specimen was prepared for testing. In addition to the saw-cut samples, standard cylindrical gypsum specimens, consistent with the way as the gypsum faults, and standard sandstone specimens were fabricated for mechanical testing. Two samples were prepared under different test conditions to minimize the effect of sample heterogeneity on the experimental results.

Triaxial tests were performed at room temperature using a servo-controlled MTS815 tester without any pore pressure (Figure 1A). The confining pressure was applied through silicone oil in the triaxial cell. The sample was wrapped with a polyolefin sleeve to separate it from the silicone oil. Axial forces were measured using force transducers with a maximum load capacity of 2200 kN and an accuracy of ±0.5%. Circumferential strain ε r was consecutively measured using circumferential extensometers with a measuring range of +12.5 mm, −2.5 mm, and an accuracy of ±0.5%.

Uniaxial and triaxial compression tests were first performed on gypsum and sandstone standards, followed by triaxial compression tests on sawed samples. The experimental procedure is as follows: First, the confining pressure was applied at a rate of 2 MPa/min until it reached the set value of 10 MPa. The confining pressure was then kept constant, and the axial load was applied at a fixed displacement rate of 0.01 mm/min, corresponding to a strain rate of approximately 1.67 × 10 − 6   s − 1 . The procedure was terminated when the specimen deformation gradually stabilized. After the tests on saw-cut samples with different dip angles, additional tests were conducted on 60° saw-cut samples under various confining pressures (5, 10, 20, 40 MPa) and at different loading rates (5E^-3, 1E^-2, 2E^-2, 4E^-2, 8E^-2mm/min) under a constant confining pressure of 10 MPa. At the end of the experiment, the surface morphology of the fault was reconstructed using a non-contact tomography scanner, and the roughness of the surface fracture was analyzed.

The stress‒strain curves provide valuable insights into the evolution of the mechanical properties of the specimens under loading. Table 1 shows the basic physical properties of the sandstone and gypsum used in this laboratory test. Figure 2A presents the uniaxial compressive stress‒strain curves of intact sandstone and gypsum specimens. The fractures of both sandstone and gypsum exhibit typical brittle characteristics. The uniaxial compressive strength of sandstone is 67.22 MPa, approximately 3.3 times that of gypsum. The elastic modulus of gypsum is 1.7 GPa, which is much smaller than that of sandstone (10.52 GPa). The deformation of gypsum specimen during the initial stage of pore compaction is significantly larger than that of sandstone specimen due to its higher porosity. Figure 2B shows the differential stress-strain curves of 60° saw-cut samples with and without gypsum faults. Due to the consolidating effect of gypsum, specimens with gypsum faults exhibit significantly higher shear strength compared to those without gypsum. Moreover, the specimen with a gypsum fault undergoes stick-slip behavior upon activation, while the specimen without a gypsum fault undergoes stable sliding after activation.

Figure 6 illustrates the fracture morphology and types of cracks after the failure of intact rock and saw-cut specimens. All specimens containing gypsum faults suffered severe damage; however, the fractures in sandstone varied significantly with different β angles (Figure 6A). For intact sandstone, it primarily exhibits brittle cracks at an angle of approximately 72° to σ 3 direction. In contrast, the fractures of specimens at β of 0°, 15° are similar to those of intact sandstone, with macroscopic cracks traversing the fault, however, the fracture angles decrease to approximately 60° and 50°, respectively (Figure 6B). Fractures originate from tensile wing-shaped cracks starting from the saw-cut surface, extending to both sides, and eventually intersecting with symmetric cracks on the back of the specimen. In specimens at β of 30°, 35°, the angle between the main crack and the saw-cut surface further decreases to approximately 30° and 20°, respectively. No main cracks were observed on the surfaces in specimens of β between 45° and 65° (Figure 6A). At the β of 45°, microcracks were observed in the rocks on both sides of the fault. Meanwhile, fractures within the gypsum fault were observed at β of 45°, 50°, and 65°, which may be related to the deviation from the optimal dip angle for fault slip, leading to shear cracks within the gypsum fault (Figure 6C). In contrast, at the β of 55°, 60°, no microcracks were observed in the rocks on both sides of the fault, and no fracturing occurred within the gypsum fault. The gypsum fault completely separated from the sandstone matrix on one side and slid along the contact surface between the two (Figure 6C).

The statistical parameters are commonly used to evaluate the morphology of rock fractures or sawed surfaces can be directly derived from the data coordinates of the asperities on the fracture surface. The statistical parameters typically include the root mean square of the height of the profile R q (Equation 2), the peak asperity height R z (Equation 3) in the amplitude characteristics; and the root mean square of the first derivative of the profile Z 2 (Equation 4). R q = 1 N ∑ i = 1 N z i − z a 2 1 2 (2) R z = z max − z min (3) Z 2 = 1 N − 1 ∑ i = 1 N − 1 z i + 1 − z i 2 x i + 1 − x i 2 1 2 (4) where z i represents the surface height at point i , N is the number of sampling points, z a is the distance between the profile and the mean elevation line, z max is the maximum surface height, z min is the minimum surface height, and ( x i , z i ) and ( x i + 1 , z i + 1 ) are the coordinates of the two adjacent points on the fracture profile. In addition, the Joint Roughness Coefficient (JRC) is calculated using an empirical formula (Tse and Cruden, 1979): J R C = 32.2 + 32.47 ⁡ log ⁡ Z 2 (5)

In order to calculate the statistical roughness parameter and JRC (Equation 5), 26 equally spaced fracture profiles were extracted from each fault surface along the direction parallel to the fault. The average roughness parameters and JRC for the 26 profiles are listed in Table 4.

After experiments, both sandstone layer and gypsum layer were subjected to non-contact tomography scanner and reconstruction (Figure 7). In addition to the surface cracks mentioned earlier, it was also observed that the surface of the gypsum was significantly smoother than that of the sandstone, attributed to the differing grain sizes of the sandstone and gypsum particles. This was corroborated by the roughness calculations (Table 4). A clear slicken line was observed parallel to the slip direction on the surface of the sandstone layer, which occurred due to the fracture and displacement of asperities on the sandstone layers. Its visibility increased with higher P c or lower β angle, which is related to the stress state on the fault surface, and will be discussed in more detail. The roughness of the fracture surface was significantly greater than that of the shear surface (Figure 8A), with the complete inter-rock fracture particularly triggered by the 0° fault. As P c increases, it was observed that the roughness of the gypsum layer decreases, while the roughness of the sandstone layer increases (Figure 8B). This occurs because the deformation modulus of the gypsum layer is greater, and compaction under high normal pressure reduces the asperity height of the gypsum layer. The fracture and displacement of asperity on the sandstone surface increased the roughness.

The differences in fault surface morphology are closely related to the fracture and stick-slip patterns of the fault. In the following sections, we will discuss in detail the impact of fault dip on shear strength of saw-cut specimens, as well as the mechanisms of confining pressure and loading rate on the stick-slip state of the fault. The correlation of experimental results with underground engineering near in-situ faults is also discussed.

Based on the relationship between shear stress and normal stress components on the fault surface under different P c for the 60° fault (Figure 1B), we fitted the friction coefficient and cohesion of the contact surface with gypsum faults (Figure 9A). According to the single structural plane strength criterion (Jaeger, 1960), when the fault dip angle is equal to = 45 ° + γ / 2 γ = 90 ° − tan − 1 1 / μ , i.e., β = 58 ° , this represents the optimal dip angle for fault slip. When β 1 36 ° < β < β 2 80 ° , the specimen will slip along the fault plane. When the fault dip angle is outside this range, the maximum differential stress of the rock containing the fault equals that of the intact rock. This value can be obtained through the internal friction angle φ and cohesion c 0 of the rock matrix (Table 1), as given by Equation 6: σ d = 2 c 0 ⁡ cos ⁡ φ + 2 σ 3 ⁡ sin ⁡ φ 1 − sin ⁡ φ (6)

For a fault containing cohesive fault gouge (Fagereng et al., 2010), the maximum differential stress required for its activation is: σ d = tan ⁡ β + c o t β / 1 − μ ⁡ cot ⁡ β c w + μ σ 3 (7) Where σ 3 is the minimum principal stress, μ is the friction coefficient of pre-existing fractures, β is the fracture angle relative to σ 3 , c w is the cohesive strength of the fault gouge.

Therefore, based on Equations 6, 7, we can calculate and predict the differential stress at failure for rocks containing cohesive faults (Figure 9B). Within β ranging from 0° to 40°, the maximum differential stress in saw-cut specimens decreases gradually as increasing β angle from experimental observations. The presence of gypsum layers with finite thickness, unlike the theoretical assumption of infinitesimally thin faults, alters the mechanical properties of the sandstone. In β of 0°–30°, since the cohesive strength of the gypsum is significantly lower than that of the sandstone, the presence of gypsum fault changes the overall cohesion of the saw-cut specimen and affects the friction angle during failure, resulting in cracks through the gypsum layer having angles lower than the internal friction angle of intact sandstone specimens (Figure 6). In β at 35° and 40°, closer to the optimal slip angle for fault activation, the fault locking effect of the faults is unstable. For instance, during the linearly increased stage of the specimen under stress, some slight stress drops were observed, indicating sliding between the fault surfaces. In β ranging from 45° to 65°, the deviation between theoretical predictions and experimental results may be attributed to the rotation of stress within the gypsum faults (Giorgetti et al., 2019). This is influenced by the variation between the direction of maximum shear stress and β angle, with internal cracks within the fault corroborating this observation (Figure 7). Compared to unfilled saw-cut samples (Guerin-Marthe et al., 2023; Meng et al., 2023) or saw-cut samples with fault clay gouge (Giorgetti et al., 2019), the presence of internal cracks within the gypsum faults at 45° and 50° indicates that the sliding surface is not a two-dimensional plane. Faults slide along newly formed surfaces, increasing the roughness between faults and consequently increasing the friction coefficient. Thus, this alters the distribution of shear and normal stresses on the fault surfaces, requiring a higher differential stress for fault activation.

Based on the previous analysis, β exceeding 40° consistently exhibit a fixed amplitude of stick-slip behavior. However, the trends in differential stress before and after fault activation vary. Importantly, the differential stress trends under different P c closely resemble those β of 45°–60°. The differential stress during this stage was extracted (Figure 10). The figures identify four main modes of stick-slip from fault activation. These modes are: Type 1, depicted in Figures 10A, E, featuring a sharp drop at fault activation; Type 2, shown in Figures 10B, F, featuring a slow decrease with irregular multi-peak behavior at fault activation; Type 3, illustrated in Figures 10C,G, H displaying a cyclic decrease around fault activation; and Type 4, shown in Figure 10D, demonstrating a cyclic and steady decrease around fault activation.

The characteristics of stress drop during fault activation are correlated with the stress field distribution on the fault plane. Under lower β or higher P c , the fault plane commonly exhibits higher normal stress. The interlocking effect between the gypsum fault crack and the sandstone layer results in static friction significantly exceeding sliding friction. Higher normal stress leads to tighter contact between the surfaces, resulting in stronger adhesion and interlocking of rough particles, thereby increasing the static friction coefficient. The combined increase in friction coefficient and normal stress necessitates a higher shear force for fault activation. At the same time, greater shear force accumulates stronger sliding potential energy, increasing the speed of frictional rupture (Brantut et al., 2016). Therefore, a Type 1 or Type 2 stress drop occurs upon fault activation. Influenced by decreasing P c or increasing β , the decrease in roughness of the sandstone layer and reduction of normal stresses also cause the fault to transition from dynamic destabilization to progressive fault activation (Type 3). At 65°, lower normal stresses and lower roughness allow static friction to approach sliding friction, thus producing a Type 4 change characteristic.

The correlation between the rate of faults and stress forms the basis for studying fault instability. During the specimen loading process, the radial deformation of the specimen is mainly influenced by three factors: first, lateral expansion during loading, primarily controlled by the material’s inherent Poisson’s ratio; second, the main fracture produced by sandstone failure under the influence of low-angle faults, and the deformation caused by continuous opening of fractures; third, the relative sliding between pre-existing faults under the influence of high-angle fault sliding. For β above 45°, the lateral displacement before fault activation is minimal. Therefore, during the fault sliding process, the radial displacement caused by the deformation of sandstone due to the Poisson effect is negligible. Consequently, the change in radial displacement can be used to reflect the fault slip displacement. For faults in the slip stage, according to the trigonometric relations, the relationship between radial displacement and fault slip is as Equation 8: ∆ s = ∆ l − 2 π r 4 ⁡ cos ⁡ β (8) where ∆s is the fault slip displacement, ∆l is the circumferential displacement during the slip stage, r is the radius of the cylindrical sample. The slip rate of the fault is defined as the first derivative of displacement with respect to time. Figures 11A–C present the variations in fault displacement and slip rate during fault sliding processes at different β angles, P c , and loading rates, respectively.

Each fault stick-slip event is accompanied by stress drop and acceleration/deceleration of the fault, since there is a positive correlation between fault slip rate and stress drop (Guerin-Marthe et al., 2023). This results in a higher slip rate during fault activation for lower β and higher P c . Notably, faults under 40 MPa P c show several accelerations before complete activation (Figure 11B). This occurs because high P c and shear stress can cause localized rupture of asperities, triggering occasional accelerations. For faults under loading rates of 5E^-3 - 4E^-2, although the magnitude of stress drop decreases with increasing loading rate, the average and maximum slip rates remain nearly the same. This indicates that the loading rate primarily influences fault displacement through the stick-slip cycle. When the loading rate reaches 8E^-2 mm/min, the fault slip rate does not drop to zero (Figure 11C), proving that the fault stops stick-slip and transitions into stable sliding at a certain loading rate. It is likely that as the loading rate continues to increase, the slip rate of the fault becomes primarily associated with the loading rate, and the fault will continue to slide along with the displacement of the platen. The preceding discussion demonstrates that the maximum slip rate of the laboratory fault is mainly controlled by β and P c , while the loading rate primarily regulates the stick-slip cycle of the fault.

Although our study was conducted in a laboratory, work on rock damage processes from the laboratory-scale to the Earth-scale is very common (Ke et al., 2018; Xu et al., 2023). Our observations indicate that low-dip faults cause significant stress accumulation within the surrounding rock mass, resulting in increased damage to the rock mass and expanding the extent of the fracture zone around the fault core. This not only reduces the stability of the surrounding rock mass in projects (Su et al., 2017), but also increases the porosity and permeability of the rock mass (Hou et al., 2024), raising the risk of water and mud surges (Zhang et al., 2024) in mines, tunnels and other projects. High-dip faults have a stronger tendency to slip, and sudden fault activation may trigger localized seismic shaking (Cao et al., 2024). In addition, as resource extraction goes deeper (Wang et al., 2017), high confining pressure in deep can places faults under greater critical stress, which may lead to localized rupture and episodic acceleration. There is also greater rupture velocity when the fault is fully activated. Furthermore, due to the stress field in deep rock masses (Pan et al., 2023), stress redistribution caused by fault destabilization (Ju et al., 2022) lead to dynamic hazards such as rockbursts and coal and gas outbursts (Bai et al., 2022). The laboratory loading rate reflects the construction speed and excavation cycle of underground projects (Liu et al., 2024), and the choice of construction strategies influences the stress and slip states of the fault (Rasouli et al., 2011). Therefore, geological exploration and monitoring should be emphasized in the design and construction of underground engineering. During construction, excavation progress and roadway support design should be adapted to the specific geological conditions. Additionally, emergency measures should be designed and optimized. These measures are essential to ensure the stability of the fault and the safety of the corresponding underground engineering.