In light of the economic growth observed in numerous countries, the demand for coal, along with its extraction capabilities, continues to increase. This upsurge has led to intensified mining activities and deeper excavations, which in turn have amplified the complexity of safety challenges linked to geological conditions in coal mines. Manifesting in diverse forms such as coal bursts, gas outbursts, roof collapses, and water inrushes, these challenges are particularly prevalent within fault activation zones (Hu et al., 2014; Mark & Gauna, 2016; Wang et al., 2018; Zhou et al., 2023). Faults, which are prevalent in coal mines, interrupt the continuity and integrity of rock layers, and their activation significantly impacts the safety of coal mining operations. The stability of these faults is influenced by a multitude of factors, including the mechanical behavior and mineral composition of fault gouges, the hydraulic pressures within fault zones, and the prevailing stress conditions (Bao & Eaton, 2016; Delle Piane et al., 2016; Ding et al., 2023; Hu et al., 2014). Roadway instability in mines, especially those compromised by faults, presents formidable challenges (Dou et al., 2019). These faults, when disturbed by mining, are prone to low strength, high deformability, and activation, leading to severe deformation of the surrounding rock in the affected areas. Nevertheless, the mechanisms driving fault instability upon unloading remain elusive, underscoring the urgent need for research into the instability and failure of surrounding rocks triggered by subterranean excavation (Wu, 2021).

A multitude of studies have delved into simulating tunnel conditions within fault zones, each addressing distinct issues and collectively enriching this field of research through mechanical models (Ou et al., 2022) numerical simulations (Han et al., 2021; Zhang et al., 2017) and laboratory experiments (Li, Liu, et al., 2021; Zhang et al., 2021; Zhao, Zhang, et al., 2020; Zhao et al., 2023). In the realm of mechanical modeling, Wang et al. (2020) developed a mechanical model to delineate stress distribution in front of the driving face during coal roadway excavation, emphasizing the critical influence of tunneling speed on coal and gas outburst accidents near the tunnel face. Li, Dai, et al. (2021) assessed the stability of underground caverns influenced by bedding planes using catastrophe theory. Shan et al. (2023) formulated a mechanical model that accounts for fault slip triggered by principal stress unloading, premised on plane strain conditions. Turning to numerical modeling, Kang et al. (2021) highlighted the pivotal role of stress distribution near the fault in ensuring the safety and stability of roadway excavations with 3 Dimension Distinct Element Code. Building upon this, Vardar et al. (2021) investigated how roadway excavation disturbances activate faults, studying the resulting stress distribution and rock deformation around these fault zones. Han et al. (2021) introduced a novel combined finite-discrete element method to elucidate the location and dip angle of faults in rockburst development around tunnels. Zhang et al. (2017) shed light on the instability mechanisms of faults under mining disturbances using Universal Distinct Element Code software, while Shang et al. (2021) investigated the impact of fault angle on stress distribution and failure modes in surrounding rock using PFC2D.

The previous studies have identified the low-strength fractures within faults, which deteriorate and expand due to mining activities, as the primary factors contributing to the instability of surrounding rock. Wang et al. (2019) embarked on a study of sudden fault slips and instability triggered by coal mining, using a physical test with two fault structures. Meanwhile, Wu et al. (2017) undertook both experimental and numerical analyses on a simulated granular fault. Their aim was to decipher the mechanism behind excavation-induced seismicity. Their findings revealed a marked reduction in both normal and shear stresses as the fault approaches a critical stress state. Duan et al. (2019) analyzed the effect of inclination angle change on the failure process of a fractured sample with fixed matrix and fracture properties by triaxial compression testing and discrete element modeling. Peng et al. (2020) proposed the AHP-Cloud model to evaluate the risk level of water inrush of the tunnel caused by fault reactivation and summarized the mechanisms involved. Therefore, it is crucial to conduct an in-depth study on how tunneling parameters influence fault stability during excavation.

Numerous studies have investigated fault instability under various conditions, and yet research into fault instability specifically induced by roadway excavation remains scarce, particularly concerning the correlation between laboratory- and field-scale fault activation mechanisms. This research primarily aims to examine tunnel stability within fault zones, considering factors such as excavation speed and fault angles. To this end, a mechanical model simplified the fault mechanics environment, while PFC2D analyzed how excavation parameters affect fault stability. Additionally, a stress rate relationship was established across laboratory and field scales, adhering to the principle of similarity.

2 PROJECT BACKGROUND

The Zhengli Coal Mine is located 10 km southeast of Lanxian County in Shanxi Province, China (Ma et al., 2021). The primary coal seam within Zhengli Coal Mine is identified as No. 4–1# coal seam with an average mining depth of 650 m which belongs to the Shanxi Formation of the Carboniferous System. The coal seam thickness is 1.0–1.4 m, the average coal thickness is 3.5 m with a dip angle between 6° and 10°. The histogram of the top and bottom of the coal seam is shown in Figure 1.

           

In Panel 103, minor faults constitute the predominant geological structures, with faults F36 and F37 exerting the most significant impact on roadway excavation, as depicted in Figures 2 and 3. The aim of this paper is to evaluate the effect of these two faults on the stability of roadways. The parameters associated with the faults under study are detailed in Table 1.

           

           

From Figure 3, it can be observed that the surrounding rock lithology of the roadway is coal and sandy mudstone (Ma et al., 2021). It is assumed that the surrounding rock of the roadway is sandy mudstone, with a uniaxial compressive strength of 41 MPa, and the Young's modulus is 29 GPa with a density of 2.65 × 103 kg/m3. It is also assumed that the tensile strength sandy mudstone is one-eighth of the compressive strength, which is 5.1 MPa and it is assumed that the mechanical properties of the fault are consistent with mudstone. The uniaxial compressive strength is 11 MPa, and the tensile strength is assumed to be one-eighth of the compressive strength, which is 1.4 MPa. The Young's modulus is 10 GPa.

Assuming that both the sandy mudstone and the fault satisfy the Mohr–Coulomb shear strength criterion, the Mohr–Coulomb shear strength values for sandy mudstone and the fault are ${\tau }_{\text{sandy}}=7.2+{\sigma }_{\text{sandy}}\tan 51°$ and ${\tau }_{\text{fault}}=2+{\sigma }_{\text{fault}}\tan 50°$ respectively, from Equations (1) and (2).

To ensure safe and efficient mining when these roadways pass through the F36 and F37 faults, the impact of roadway excavation speed on the stability of various inclination faults was investigated using theoretical and numerical simulation methods in this study.

3 MECHANICAL MODEL

In the context of roadway construction intersecting a fault, the deformation of the surrounding rock is contingent upon the fault stability. Conversely, the fault stability is also impacted by excavation parameters, such as the speed of excavation and the angle of inclination between the roadway and the fault. A mechanical model has been developed to simplify the complexities of the on-site roadway project. This model facilitates the examination of fault stability under various unloading conditions and fault parameters, enabling the proposal of viable excavation parameters. These parameters aim to provide practical guidance for the safe operation of coal mines. It is observed that both the hanging wall and the footwall of the fault remain stable and unaffected by the excavation activities. The study area, modeled as a 5 m by 5 m square, adheres to the plane strain assumption, allowing the stress state within the fault area to be depicted in Figure 4.

           

           

Where, ${\sigma }_r$ and ${\sigma }_{\theta }$ are the elastic radial and elastic tangential stress in front of the roadway, respectively; ${\sigma }_0$ is the in situ rock stress and the stress assumes consistency with Heim hydrostatic pressure ( ${\sigma }_0$  = 17.5); $r_0$ is the radius of the cylinder model; and $r$ is the distance from the center of the cylinder to a point in front of roadway.

Figure 5 illustrates the plastic stress distribution characteristics in the rock mass ahead of the roadway. Figure 5a presents a schematic of the roadway excavation process, while Figure 5b details the stress distribution profile along the roadway, which progresses from right to left. The green dashed line in Figure 5b indicates the plastic tangential stress distribution ahead of the roadway head; the yellow dashed line represents the plastic radial stress distribution in the same region. The green solid line shows the plastic tangential stress and the yellow solid line shows the plastic radial stress. Research indicates that the concentrated stress coefficient at the roadway face is 3 (Li et al., 2018, 2019; Xu et al., 2019) signifying that the maximum plastic shear force is denoted by 52.5 MPa. In practical applications, an advancing-induced stress exceeding 5% of the initial rock stress defines the excavating disturbance radius. When integrated with the aforementioned physical parameters, the influence distance of the roadway is given by L1 = 8.7 m. Given the relatively small plastic range compared to the elastic range, calculations are simplified by assuming that both the maximum plastic shear stress and the minimum radial stress occur at the roadway working face's surface. The affected area's plastic shear force slope in the direction of excavation is k1 = −2.01 MPa/m and the plastic radial force slope is k2 = 4.02 MPa/m. Considering various excavation methods (roadway excavation speeds range from 1.2 m/day for the drilling and blasting method to 12 m/day for the driving and bolting integration method), the daily advancement rates for the roadway are established at 2.4, 4.8, 7.2, and 9.6 m/day for a 12-h workday, corresponding to 0.055, 0.110, 0.117, and 0.222 cm/s, respectively.

After substituting the roadway excavation speed into Equations (11) and (12), with advancing speeds of 0.055 0.110, 0.117, and 0.222 cm/s, the change rates of radial stress at point A are −0.111, −0.222, −0.335, and −0.447 kPa/s, respectively. The change rate of tangential stress at point A is 0.223, 0.447, 0.670, and 0.893 kPa/s.

By substituting different stress loading rates into Equations (7) and (8), the trend lines of normal stress and shear stress changes on the fault plane can be obtained under advancing-induced stress loading and unloading conditions for different fault angles, as shown in Figure 6.

           

From Figure 6, it can be observed that the blue dashed line represents the Mohr–Coulomb strength envelope of the bedrock, while the red dashed line represents the Mohr–Coulomb strength envelope of the fault. Point A corresponds to the initial stress state, which means that when both horizontal and vertical stresses in the research area are 17.5 MPa, it represents the stress state on the fault plane. The behavior of normal and shear forces on the fault plane during loading is characterized as follows: For fault angles greater than or equal to 60°, normal stress diminishes with prolonged loading, whereas for fault angles less than 60°, normal stress increases as loading time increases. Additionally, at fault angles of 0° and 90°, the shear force on the fault plane consistently remains at zero throughout loading. Conversely, for all other fault angles, the shear force components on the fault plane intensify with continued loading.

Overall, as the loading progresses, the stress on the fault plane always remains below the Mohr–Coulomb envelope of the bedrock and the fault, indicating that shearing slip of the fault will not occur, ensuring the stability of the fault. However, the theoretical study assumes that both the bedrock and fault are isotropic and overlooks the impact of the stress loading rate on the stability of the fault. Based on this work, the PFC2D numerical simulation will be used to study the heterogeneity, loading rate, and the effects of fault angle on fault crack propagation and distribution characteristics.

4 NUMERICAL SIMULATION

The Particle Flow Code (PFC) method is utilized for simulating the mechanical behavior of rock and soil, incorporating prevalent contact constitutive models such as the linear model, the linear contact bond model, and the linear parallel bond model (Cundall & Strack, 1979). In this mode, the linear model and the linear parallel bond model are employed.

Physical quantities such as dimensions, stresses, and elasticity are based on the similarity principle in previous numerical and experimental laboratory model tests, making sure that the physical features of the model resemble those of the field (Lin et al., 2015). The key element of the similarity principle is the similarity constant (C), which represents the ratio of field (f) to model (m) physical entities. The numerical simulation model test for roadways crossing the fault in this research has several crucial similarity constants, which include the following:

For this paper, the field geometry is a square measuring 5 m on each side. The numerical model used had a square shape with a side length of 5 cm, which means that the geometrical similarity ratio was 1. By applying the equations from Equations (13) to (21), we were able to determine the parameters of the physical quantities required for the numerical simulation. These parameters are listed in Table 2.

To ensure the reliability and accuracy of the model, uniaxial compression and Brazilian tensile PFC2D experiments were carried out according to the results of Table 2, as shown in Figure 7. Specifically, the numerical simulation parameters are shown in Table 3.

           

From Figure 7, it can be seen that the elastic modulus, compressive strength, and tensile strength of the numerical model are consistent.

According to the similarity criterion, the size of the numerical model is a square with a width of 5 cm. The top boundary and the right boundary are stress boundaries, while the left boundary and the bottom boundary are roller constraints, as shown in Figure 8. From the Project Background and the similarity criterion, we can determine the basic mechanical parameters of Sandy Mudstone and the fault in the numerical simulation, as shown in Table 3. A total of 4639 balls are generated in this model. The fault rotates around point A as the center, with an angle of rotation. The number of contacts on the fault is 70, which will vary with the length of the fault.

           

To investigate the impact of excavation speed and the angle of the fault on the stability of the fault, the orthogonal experimental method is used to obtain the numerical simulation experiment scheme, as shown in Table 4.

Relative to the control group without faults, samples with faults in this study are all referred to as the experimental group. Besides the 28 experimental tests listed in Table 4, this study also conducted numerical simulations for control groups with horizontal stress rates of −1.11, −2.22, −3.35, and −4.47 Pa/s and vertical stress rates of 2.23, 4.47, 6.70, and 8.93 Pa/s. In the numerical models, the stress loading path of the specimen is as follows: the vertical and horizontal stresses are first loaded to 17.5 MPa. After a period of stabilization, stress was loaded and unloaded according to the specifications in Table 4, as illustrated in Figure 9.

           

5 RESULTS

All the crack counts from the numerical experiments were compiled, as shown in Table 5 and Figure 10.

           

In Figure 10, the y-axis represents the number of cracks, while the x-axis represents fault angles. In the following discussion, tests without faults are collectively referred to as the control group, while tests with the presence of faults are referred to as the experimental group. The solid line and the dashed line represent the crack count for the control group and the experimental group with vertical stress rates of 2.23, 4.47 6.70, and 8.93 Pa/s. In all experimental groups, the number of cracks in groups with faults surpasses those without faults subjected to equivalent stress rates. Notably, in every experimental group, the proportion of tensile cracks exceeds 80% after calculation, signifying that the dominant failure mode within the study area is tensile. At a constant fault angle, as the stress rate increases, the count of tensile cracks decreases, suggesting a more comprehensive sample failure with prolonged loading durations. Interestingly, at a consistent fault angle, the number of shear cracks remains unaltered with variations in the loading rate, indicating that the shear failure remains unaffected by the stress rate. As the fault angle increases, the shear cracks within the fault show a tendency to fluctuate up and down with small fluctuations. Among them, when the fault angle is 90°, the maximum number of shear cracks is 49, while at a fault angle of 0°, the number of shear cracks is the least, totaling 38. However, the total number of fault contacts is only 70, which implies that as long as there is a fault, it will be fully activated under the influence of roadway advancing.

From an energy perspective, assuming that each crack releases the same amount of energy, it means that the crack counts represent the amount of energy released. The larger the stress rates, the more energy the sample absorbs per unit time, but the fewer cracks there are, indicating that the sample has a greater storage capacity (Gong et al., 2022; Zhou et al., 2023). When a roadway crosses a fault, rockburst accidents are more likely to occur, posing challenges in such geological conditions. Fault angles significantly influence crack counts. Yet, due to the uncertain spatial distribution characteristics of fractures, it is impractical to determine the extent of fault activation based on crack counts influenced by fault angles.

To gain a deeper understanding of the spatial distribution and inclination characteristics of the cracks, spatial distribution diagrams and rose diagrams detailing crack inclination were sequentially discussed. Considering the extensive experimental data and the comparative influence of fault angles on the distribution characteristics of cracks and displacements relative to the vertical stress rate, a vertical stress rate of 8.93 Pa/s was chosen as a representative case for discussion in this paper.

From Figure 11, it can be observed that, in the group without fault, the specimen shows only tensile cracks, and these cracks are uniformly distributed. In the groups with fault, shear cracks primarily occur near the fault plane. As the fault angle increases, tensile cracks gradually converge toward the fault plane, and yet almost no cracks form in the immediate vicinity of the fault.

           

Figure 12 presents a radar chart of crack inclination angles. For clarity in the results, the minimum crack value is set at −20°. Cracks with an inclination of 180° are equivalent to those with an inclination of 0°. It can be observed that in all the experimental groups, the predominant crack inclination is between 90° and 100°, parallel to the vertical stress. The angle of cracks is influenced by the fault, and as the fault angle increases, the number of horizontal cracks gradually increases. However, it remains significantly fewer than the number of vertical cracks.

           

Fault activation typically results in the formation of shear and tensile cracks. Shear cracks are primarily found within the fault plane. With an increase in fault angles, there is a gradual build-up of tensile cracks adjacent to the fault plane, a trend that becomes more pronounced at a fault angle of 60°. The distribution of shear cracks angles is uniform, suggesting that internal fault cracks are fully activated regardless of angle changes (Xu et al., 2019). Tension cracks, predominantly aligned with vertical stress, suggest that even if future development connects cracks in the same direction, the overall integrity of the surrounding fault rock remains intact. An increase in fault angles leads to an accumulation of tensile cracks near the fault plane, which in turn promotes fault activation. The higher the activity of the fault, the greater the likelihood of significant deformation of the roadway, potentially leading to increased maintenance costs.

The relationship between the counts of tensile and shear cracks does not show a linear correlation with fault angles. To further comprehend the association between crack counts and fault angles, focus is directed toward the displacement in specimens with different fault angles, as illustrated in Figure 13.

           

In Figure 13, the black arrows represent the direction of the displacement vectors, and the color of the contour indicates the absolute value of the displacement vector. It is evident that the overall displacement is moving toward the bottom-right. Specifically, the upper part of the specimen primarily displaces vertically downward, while the lower part mainly shifts horizontally to the right. This behavior aligns with the stress environment of the specimen. Experimental groups with faults show a greater maximum displacement than the control groups without faults. As the fault angle increases, the relative displacement between the upper and lower plates of the fault becomes more pronounced. At 60°, the difference in the relative displacement between the upper and lower plates of the fault is the most significant. This trend is consistent with the variation in the number of tensile cracks within the specimen, suggesting that a larger displacement difference contributes to an increase in the number of tensile cracks.

In conclusion, the fault angle is a critical factor affects maintenance costs post-roadway excavation, primarily through its impact on the number of shear and tensile cracks near the fault surface. Additionally, the speed of excavation plays a significant role in the potential for rock bursts by affecting the energy accumulation within the surrounding fault rocks. Consequently, in the Zhengli Coal Mines, where roadway excavation intersects faults, moderating the excavation speed and deliberately reducing the angle between the roadway and the fault can substantially mitigate the risk of rock bursts and associated maintenance expenses. These findings are consistent with contemporary research (Song & Liang, 2021; Zhao, Yu, et al., 2020) and offer valuable theoretical insights for the planning of roadway excavations in coal mines.

6 CONCLUSIONS

CONFLICT OF INTEREST STATEMENT

The authors declare no conflict of interest.