2.1 Rock specimen and data sources

A large amount of test data pertaining to the shear performance of bolted rock joints has been collected from research reports. The prominent attributes of the bolted rock joint, along with the associated experimental conditions, are meticulously delineated in Table 1. The details provided include rock material, rock mechanical properties, joint roughness, rock bolt materials and properties, grout materials, bolt angles, and normal stress. Rock joint specimens can be classified into two types: (1) real rock specimens, which include granite, limestone, sandstone, and others, and (2) rock-like materials, which include concrete, plaster, and so on. The dimensions of the rock joint test specimen are as follows: length: 100–200 mm; width: 100–150 mm; and height: 50–150 mm. The length-to-width ratio is maintained at 1 to 2.

2.2 Rock joint sample preparation

The preparation of a rock joint sample is a crucial aspect for the bolting rock joint. The preparation methods can be categorized into splitting, abrasive, engraving, and 3D printing methods, based on the working principle of the preparation process. (1) Splitting method: This approach involves the prefabrication of symmetrical cracks on the rock specimen, followed by the application of a concentrated line load to induce split and fail in the rock. Although this method can obtain the original 3D joint, it is incapable of reconstructing the joint (Figure 2b). (2) Abrasive method (Jiang et al., 2021; Li et al., 2021): This method entails the construction of an abrasive tool with joint surface morphology, followed by the preparation of two-half specimens by pouring rock-like materials (Figure 2a). Abrasive tools are typically made of steel or plaster, enabling the production of numerous identical specimens through a simple operation. However, this method can only create sample 2D rock joints. With technological advancement, materials with good plasticity, such as silicone, are also utilized to create more complex joint models. (3) Engraving methods (Cheng et al., 2021; Wang et al., 2020; Zheng et al., 2021): This technique involves the construction of a digital model of the complex 3D joint surface using 3D scanning, Synfrac software, and so forth. Subsequently, the joint surface point cloud data are converted into engraving path data to control the cutter head to automatically engrave the rock sample. Ultimately, complex rock joint surfaces are reconstructed. This method enables the repeated production of rock joint specimens that mirror the original rock joint in terms of lithology, joint morphology, and mechanism (Figure 2c). (4) 3D printing method (Figure 3) (Cheng et al., 2022; Zhang et al., 2022): The 3D digital models of the rock joint samples are first established, and then the same jointed rocks are produced using 3D printing technology. This method can produce jointed rock samples, but the limitations of 3D printing materials may affect sample strength.

               

               

2.3 Mechanical tests

At present, the majority of experimental devices are primarily designed to apply normal axial stress and displacement (Table 2 and Figure 4). Moreover, the specimens utilized for testing predominantly adopt a cubic form. To accumulate experimental data for different normal loads, direct shear experiments are conducted on rock anchor rod specimens. This process facilitates the characterization and analysis of alterations in the shear load–displacement and shear–normal displacement curves, shear strengths, axial force of bolts, and shear failure modes of rock joints and bolts. The acoustic emission technique is equipped to monitor the microstructural failure and deformation of joint surfaces and reinforced planes during the shearing process. Digital image correlation technologies are applied to compare the mechanical characteristics of rock bolts and microstructural damage on joint surfaces subsequent to shear tests.

               

In practical engineering, the bolt system is subjected to a stress field caused by a combination of factors such as grouting pressure, crustal stress, and disturbance stress from excavation and other engineering activities. In deep underground engineering, the normal stress generated by grouting stress and mining disturbance is typically below 10 MPa. However, in shallow engineering, it is usually less than 2 MPa. Consequently, normal stress is typically applied within two ranges: 0–2 and 2–10 MPa. In this way, the rock joint specimen is exposed to direct shear, maintaining a constant normal stress and shear velocity, until it either succumbs to failure or reaches the predetermined threshold of shear displacement.

3.1 Shear force–shear displacement curve

Figure 5 illustrates the shear force–shear displacement curves of rock joints reinforced by a rock bolt under varying normal stresses and bolted angles. The curves show different shapes under different normal stresses. Under low normal stress (<2 MPa), the curves demonstrate an increasing trend with the progressive increment of shear displacement, ultimately reaching a stable state. After the rock bolt fails, the curves rapidly decrease (Figure 5a). As the normal stress increases, the curves rapidly decrease after reaching the yield point, followed by a gradual increase. Finally, the curves drop at the failure point. The shear displacement at the yield points initially increases with the increase in normal stress but subsequently decreases once the normal stress reaches 2 MPa. Within the range of 0–4 MPa, the shear displacement at the point of failure shows a rapid decline, followed by a subsequent period of stability. Furthermore, there is a notable increase in shear strength with the augmentation of normal stress. Li et al. (2023) analyzed the shear performance of grouted rebar bolts under higher normal stress (5–30 MPa) and found that the curves showed different shapes (Figure 5b). The shear stress showed a rapid linear increase until reaching peak values, followed by a mild decrease. Under high normal stress, the curves displayed more noticeable fluctuations. Figure 5c presents the shear stress curves of bolted rock joints at different bolted angles. All curves initially increase linearly and then nonlinearly at lower velocities. When the shear force reaches its peak, the curves gradually decrease. The velocities of shear force curves decrease with an increase in bolted angles. The shear strengths of bolted rock joints with bolted angles of 45°, 60°, and 75° are 59.8, 60.2, and 59.7 kN, respectively, but those with a bolted angle of 90° decrease to 55.5 kN.

               

Figure 6 presents the normal and shear displacement of bolted rock masses at various joint roughness. The normal displacement gradually increases with the progression of shear displacement. However, the magnitude of normal displacement is consistently smaller than that of shear displacement. Experiments conducted by Wu et al. (2022) found that with an increase in the joint roughness coefficient (JRC) value, the normal displacements also increase rapidly (Figure 6a,b). For example, when the JRC value ranges from 0 to 2, the maximum normal displacement is 0.32 mm. However, when the JRC value increases to 12–14, the normal displacement reaches approximately 2 mm. The bolted angle also has a significant effect on the normal displacement (Figure 6c). When the rock bolt is installed perpendicular to the joint surface, the maximum normal displacement is approximately 0.68 mm. Conversely, when the bolted angle decreases to 45°, the maximum normal displacement increases to 1.00 mm. The choice of bolt material shows a relatively minor influence on the normal displacement. The normal displacement of the basalt fiber-reinforced polymer bolt is approximately 0.80 mm, while that of the steel bolt is 0.68 mm. Rough joints have anisotropy, so the direction of shear also has some influence on the shear behavior of rock joints (Figure 6d), during the stage of shear displacement ranging from 0 to 0.5 mm, there is a decreasing trend in the normal displacement of rock joints, because the jointed rock mass does not receive the normal constraint of the rock bolt to slide, resulting in vertical displacement. Moreover, continuous monitoring has revealed that the normal displacement curve initially decreases and then increases during the initial shear stage.

               

3.2 Shear strength

The shear strength of bolting rock joints is affected by many factors, such as rock bolt parameters, rock properties, joint roughness, and normal stress, among others. According to other reports, the most important factors are the rock properties and normal stress. The majority of tests primarily focus on the condition where the rock strength is less than 50 MPa and the normal stress is less than 5 MPa. Figure 7 presents the correlation between shear strength and normal stress, as well as rock strength, for a variety of rock joints secured by bolts. While some studies have reported a decrease in shear strength with increasing normal stress for bolting rock joints (He et al., 2022; Pellet & Egger, 1996; Song et al., 2023), the overall trend demonstrates a progressive linear increase in shear strength with normal stress for such joints. A strong correlation (R2 = 0.859) is obtained between shear strength of rock joints and normal stress. The shear strength of the bolted rock joints demonstrates an approximate increase of 200% (4.0–5.5 MPa) as the normal stress increases up to 5 MPa. Furthermore, with a subsequent increase in normal stress to 8 MPa, the shear strength of the bolted rock joints further increases by approximately 250% (6.5–9.0 MPa) (Liu et al., 2017, 2018; Song et al., 2023). With an increase in normal stress, both the deformation of the joint surface and the extent of fracture within the rock mass on the shear plane show a corresponding increase (Cheng et al., 2021; Grasselli, 2005; Li et al., 2023). It is worth noting that the test data available regarding bolted rock joints subjected to normal stresses exceeding 15 MPa are rather limited. Moreover, an increase in the shear strength of rock joints is observed with an increase in rock strength (Li et al., 2021; Maiolino & Pellet, 2015). In general, the average values of shear strength initially increase linearly when the rock compressive strength reaches 60 MPa, and then become stabilized.

               

3.3 Rock bolt response

Figure 8a presents a schematic representation of the deformation of the internal rock bolt when either shear failure or shear displacement reaches its limit in anchoring the rock mass. Two significant points on the rock bolts warrant special attention. First, the plastic hinge point (denoted as point P), proposed by Dulacska (1972) to analyze the behavior of bolt–joint intersections (point O), is situated on both sides of the joint at the location of the maximum bending moment (Jalalifar & Aziz, 2010). The bolt–joint intersection point is positioned at the intersection between the bolt and the joint with the maximum shear force. The rock bolt shows bending in section PO, while the other sections only display small lateral deformation, as the stresses in the bolt cannot increase beyond point P due to its constraint. Consequently, the bending angle, which is the intersection angle between line PO and the bolt axis, reflects the dislocation and plastic deformation of bolts. Second, the bolt failure point, marked as point O, is the location where fractures occur due to shear or tensile forces. The failure bolt has an S shape and can fail in two ways: tensile-shear and tensile-bending failure (Wang, Wang, et al., 2021; Wang, Zhu, et al., 2021) (Figure 8b). When the bolt is subjected to both shear and axial forces, it undergoes tensile-shear failure, resulting in the creation of a shear plane on the joint surface. Conversely, when it is influenced by bending and axial forces, tensile-bending failure occurs, and the failure point is situated at the plastic hinge point.

               

Figure 8d shows the distribution of bending angles of the deformed bolts. The bending angle, defined as the intersection angle between line PO and the bolt axis, serves as an indicator of the dislocation and plastic deformation of bolts (Figure 8a). The range of bending angles primarily concentrates between 30° and 45° (Figure 8d). An analysis of the results of Wang, Wang et al. (2021) and Wang, Zhu et al. (2021) (Figure 8b,c) reveals that under the same normal stress (1.0 MPa), when the joint roughness is 3.14, the bending angle is 40.4°. However, when the joint roughness increases to 16, the bending angle decreases to 30.8°. The bending angle shows a linear decrease with the increase in joint roughness, with a slope of −0.76. The R2 of the fitting line is found to be 0.99 (Figure 8e). Moreover, under the same joint roughness (0), the bending angle is 39.2° when the normal stress is 0.5 MPa, but decreases to 37.4° when the normal stress increases to 2 MPa. The linear fit results in an R2 of 0.59 (Figure 8e). Furthermore, Figure 9 shows the relationship between rock strength and bending angle. The bending angles show significant fluctuations, which could be attributed to the concentration of rock strength between 30 and 60 MPa. Figure 10 illustrates the ratio of the bending angle and bolt yield force, which is utilized to evaluate the relationship between bending angle and bolt parameters. The ratios initially decrease as the bolt yield force increases from 0 to 10 kN, with values ranging from 4 to 8 (°)/kN. Then, the ratios become stable. When the bolt yield force is between 10 and 20 kN, the ratios are 1.5–3.0 (°)/kN.

               

               

3.4 Failure modes of joints

Figure 11 depicts the ratio of the failure area on the joint surface with and without rock bolt reinforcement, considering varying levels of normal stiffness and joint roughness. The failure area ratio serves as an indicator of the extent of damage caused by shear on the joint surface in relation to its total area. The shear resistance of the joint rock mass is attributed to the frictional resistance between the joint surfaces and the compression shear failure of the roughness features on the joint surfaces (Jiang et al., 2021; Liu et al., 2022; Ma et al., 2018). As the shear displacement increases, the joint surfaces undergo relative misalignment, and when the primary asperities fracture, the rock bolt begins to work. The rock bolt provides support until it eventually fails, at which point the joint in the rock mass enters into the residual stage. Recently, Wang, Zhu et al. (2021) used a high-resolution camera and Matlab image processing methods to determine the asperities on the joint with and without rock bolt reinforcement. Under the same roughness, the failure area ratio of the structural plane shows a positive correlation with the magnitude of normal stiffness or normal stress. When the normal stiffness increases from 0 to 0.5 GPa/m, the failure area ratio of the structural plane increases by over 40% (Figure 11a). As the normal stiffness increases, the failure area ratio also increases and tends to stabilize. Under the same normal stress, the failure area ratio increases with the increase of JRC. Furthermore, the rock bolt amplifies the failure area ratio by 1.5–2.0 times compared with the case of unbolted rock joints (Figure 11b).

               

Figure 12 shows the damage of heterogeneous rock joints with different roughness (Cheng et al., 2021). A rock joint characterized by differing rock properties on each side of the joint is defined as a heterogeneous rock joint. All joint surfaces show some degree of damage. A low JRC results in wear damage, which gradually degrades asperities. Conversely, a high JRC causes shear damage, which rapidly cuts asperities. An increase in JRC corresponds to greater amount of rock debris from wear, indicating more extensive joint surface damage. There are disparities in the failure modes on both sides of the structural planes, with variations in the quantity and size of rock debris. This suggests the presence of local variations in the strength of the same rock mass, resulting in nonuniform damage on both sides. The resistance of the rock joint depends on the failure characteristics. A low JRC fractures low-strength rock mass, while high-strength rock mass only experiences wear. The shear strength of the rock joint is predominantly governed by low-strength rock mass. A higher JRC results in more bulges and fluctuations on the joint surface. High-strength rock embedded in low-strength rock also amplifies the damage. The shear strength approaches that of a high-strength rock joint. The rock joint has an intermediate shear strength between the homogeneous ones.

               

Figure 13 presents the failure modes observed on bolted joint surfaces under different normal stress conditions (Li et al., 2023). The rock bolts are fractured due to the exerted shear force. In the vicinity of the structural planes, there is an ejection failure instigated by stress waves, resulting in the formation of pits on the rock surface that are oriented parallel to the direction of shear (Figure 13a,b,d,e). This is classified as a type of dynamic failure (Wu, Jiang, Gong, et al., 2019; Wu, Jiang, Wang, et al., 2019). Moreover, the closer the structural planes, the deeper the pits formed on the rock surface due to ejection failure. The figure also highlights an obvious spalling phenomenon in Figure 13c,f, indicating that the shear failure shows a progressive mode of failure. There are several cracks on the structural planes that are parallel to the surface of the bolt and oriented in the direction of shear. A series of rock fragments are collected, showing different shapes such as flakes, strips, debris, or powder, resulting from varying normal stresses during shearing. The fragment mass increases with normal stress (Figure 13g), indicating more intense damage at higher stress levels. In this study, an investigation was conducted on the rock powder generated on the structural planes as a result of brittle fracturing and pulverization of the rock. With the increase of normal stress, the mass of rock powder also shows a linear growth, as shown in Figure 13g, implying more damage to the structural plane at higher stress. During the shearing of anchored rock masses, both static and dynamic failures occur at the structural planes where anchor rods are connected. Dynamic failures typically show more severe damage and loud sound waves, while static failures on the rock mass surfaces are characterized by sudden stress drops and loud sounds.

               

4.1 Shear deformation process of the bolted rock joints

Figure 14 presents the shear force–shear displacement curves of rock joints with and without bolts. The curve for the unbolted sample before failure comprises four stages: compaction, elastic deformation, drop, and residual deformation. The curve for the bolted sample shows two different shapes. One shape encompasses six stages under low normal stress (<10 MPa): compaction, linear elasticity, fall, yield, strengthening, and residual deformation. The other shape, under high normal stress (10–30 MPa), consists of four stages: linear elasticity, intensification, nonlinear softening, and residual deformation. The compaction stage arises due to the friction-induced joint resistance during shearing, which compacts the area between the joint surfaces caused by the manufacturing process, weathering, and other factors. This stage does not exist under extreme normal stress. The relative slide in the joint triggers the elastic deformation stage.

               

For the bolted rock joint, the curve before failure can adopt two different shapes depending on the normal stress and other factors. One shape, under low normal stress (<10 MPa), has six stages: compaction, linear elasticity, drop, yield, intensive, and residual deformation. The compaction and linear elasticity stages are similar to those of the unbolted rock joint. The drop stage is characterized by a rapid decrease in shear force due to the activation of rock bolt resistance after joint bulges fail. The yield stage is marked by a gradual increase of shear force due to the yielding deformation of the rock bolt. The intensive stage is characterized by a rapid increase of shear force due to the intensification of rock bolt deformation. The residual deformation stage is marked by a constant shear force due to the frictional resistance of joint surfaces after the rock bolt fails. The other shape, under high normal stress (10–30 MPa), has four stages (Figure 5): linearly elastic, intensive, nonlinear softening, and residual deformation. The linearly elastic stage is characterized by a rapid linear increase in shear force until it reaches a peak value. The intensive stage is marked by a mild decrease in shear force due to the intensification of the rock bolt deformation. The nonlinear softening stage is characterized by a nonlinear decrease in shear force due to the softening behavior of rock bolts. The residual deformation stage is comparable to that of the previous shape.

4.2 Effect of rock properties on mechanical response

During the shearing process, the deformation of the rock bolt is symmetrical across the joint surface. This deformation can be separated into three parts: undeformed, elastically deformed (SP), and plastically deformed (PO) (Figure 15). The point of the maximum bending moment and the minimum shear force is Point P, also known as the plastic hinge. In the elastic deformation section, the rock bolt undergoes elastic deformation without causing failure in the rock and grouting. Conversely, in the plastic deformation section, compression leads to the failure of the rock and grouting, with the failure area progressively expanding. As rock strength decreases, the distance between two plastic hinges increases. This increase in distortion results in a tensile shear fracture in the rock bolt. However, as rock strength increases, the gap between the two plastic hinges narrows down, and the rock bolt primarily deforms under shear. This implies that the rock's high compressive strength restricts the axial displacement of the rock bolt and emphasizes the importance of the rock bolt's shear resistance. Consequently, in practical engineering, ordinary rock bolt support is susceptible to shear brittle fracture when anchoring high-strength surrounding rock. This can lead to the quick collapse of engineering rock mass, resulting in potential catastrophes (Chen et al., 2015).

               

The behavior of a rock joint with a bolt is affected by the rock strength. The rock bolt shows both dowel and restraint effects (Srivastava et al., 2019; Zhang et al., 2022). The rock bolt deforms, compressing the rock mass and grouting to generate a compaction area during shearing. As the shear displacement increases, the rock mass and grouting rapidly degrade under the compression exerted by the rock bolt. Two critical components are the plastic hinge and the point where deformation begins. The plastic hinge is the location where the bending moment reaches its maximum value. Consequently, compaction and failure areas are easily formed when rock mass has low compressive strength and cannot be prevented by rock mass or grouting. This leads to an increase in the permissible deformation and deformation section of the rock bolt before failure, increasing the bending angle with the rock's compressive strength (Figure 10) and shifting the position of the plastic hinge. The rock bolt fully utilizes its tensile strength, bearing a higher load and absorbing more energy. As the compressive strength of the rock increases, it exerts more resistance on the bolt due to its increased susceptibility to brittle failure. This makes it more challenging to form compaction and failure areas that would otherwise prevent the rock bolt from deforming and bring the plastic hinge position closer to the joint surface. As a result, the failure deformation and energy absorption of the rock bolt become less significant, and its shear strength becomes more prominent. In the shearing process, when the compressive strength is low, the tensile and shear strength of the rock bolt work together to provide higher resistance. However, the joint surface can only offer low resistance. This results in a decrease in the shear strength of the bolted rock joint, but an increase in the failure shear displacement, indicating that the joint shows ductile behavior. As the compressive strength of the rock mass increases, it can resist more pressure. Therefore, bolted rock joints show brittleness because they have reduced shear displacement but higher shear strength.

4.3 Effect of joint roughness and normal stress on mechanical response

The mechanical response of rock joints, when reinforced by a bolt, is significantly influenced by both normal stress and joint roughness. The maximum shear resistance of the rock bolt increases nonlinearly with roughness, according to an exponential function relationship, while the maximum shear displacement has a linearly negative association with JRC. As the JRC increases, the shear strength, as well as the maximum and residual shear displacement of rock joints, also increases linearly (Figure 8). This is because higher joint roughness leads to an increase in the variations of protrusions on the joint, thereby increasing the contact area. The friction force and shear strength of the rock joint are enhanced due to the effect of the higher asperity slope on the normal stress on the contact surface. With the increase in JRC, the size of the voids between the fluctuation bodies and the degree of fluctuation also increases. When shear failure occurs in the fluctuation body, the shear force rapidly decreases, and the joint plane shows brittle shear failure. The joint plane is generally smooth when the JRC value is low. The stress–strain curve displays only minor changes, and the main form of motion is sliding between the upper and lower rock blocks. The joint plane fails in a ductile way during the shear process. Wang, Zhu et al. (2021) (Figure 16) found that the joint roughness affects the rock bolt reinforcement. The rougher the joint, the smaller the bending angle, the less deformation, and the larger the axial force of the rock bolt. This means that the bolt shares more load and bears higher shear strength, thus providing less shear deformation resistance. The bending angle of the bolt is linear to JRC, and so is the shear failure displacement of the bolt. However, the bolt resistance is limited by its yield force. As the joint JRC increases, the maximum shear resistance approaches 1, which is the yield force of the bolt itself.

               

               

The bending angle of the bolt, defined as the angle between the original axis and the deformed axis of the bolt after shearing, indicates the bending deformation of the bolt under shear force. Figure 17 shows that it decreases sharply as the normal stress increases when it reaches a certain value (>10 MPa). This makes the bolt less effective at supporting the load while greatly increasing its shear strength. Under high and low loads, the joint surface fractures differently. At high normal load, the joint surface has many pits caused by ejection failure. There are also some cracks parallel to the shear direction. The joint surface is more intact and only shear failure occurs at low normal stress. These different failure modes of the joint surface under various normal stresses explain this phenomenon. The joint surface fails statically at low normal stress. The uneven parts of the joint surface slip and shear against each other, producing large rock debris. The joint surface fails dynamically at high normal stress. The uneven parts of the joint surface break under high pressure, resulting in a rapid release of tension. This ignites a stress wave that propagates throughout the rock mass. The stress wave reflects when it reaches the outer surface of the rock sample. The rock mass breaks if the reflected stress wave is stronger than its tensile strength. Moreover, a very strong stress wave can quickly eject rock particles. This is more likely to occur under conditions of high normal stress. Furthermore, compression erodes the joint surface at high normal load, creating fine rock dust. Therefore, the joint surface becomes more damaged as the normal stress increases (Chen et al., 2015; Deng et al., 2020; Li et al., 2023).

Figure 18 shows the energy absorption ratio per unit area of the bolt under different normal stress. As the normal stress increases from 0 to 2 MPa, the ratio rapidly increases up to 0.01/mm2. Then, the slope of the curve decreases gradually and tends to increase linearly with the increase of normal stress. A two-phase exponential association equation fits the average curve and displays a strong correlation (R2 = 0.868). Therefore, the shear energy absorption of the joint surface reduces as the normal stress decreases, while that of the rock bolt increases with the increase of normal stress. As the normal stress increases, the rock bolt's dowel action and shear increase rapidly and it bears the majority of the shear load and absorbs most of the shear energy when the normal stress is below 2.5 MPa. The joint surface deformation at those times is likely mainly elastic and slippage. As the normal stress increases above 2.5 MPa, the high normal stress restricts the rock bolt's deformation and increases the asperities' deformation resistance on the joint surface. Therefore, the shear energy absorption of the joint surface and total energy increase rapidly. Most of the tests are carried out under low normal stress (≤10 MPa), so the changing characteristics of energy absorption ratio under high normal stress (>10 MPa) need further verification.

               

4.4 Mechanism of the rock bolt angle on mechanical response

The tensile strength and shear strength of the bolt both contribute to the shear resistance, but provide a cohesion enhancement effect and a friction enhancement effect, respectively, because the bolt buckles and fails in shear under different situations. As the bolting angle increases from 45° to 90° (Zhang et al., 2023), the normal displacement of the rock mass decreases during the shear process (Cui et al., 2020), showing a decline of over 30%. The axial and shear forces of the rock bolt also change as the bolting angle increases. The axial force decreases rapidly by more than 60% as the bolting angle increases from 45° to 90°, but the shear force increases slowly by about 100%. However, when the bolting angle is small, the axial force is obviously larger than the shear force (three times). As the bolting angle increases, the shear force increases gradually and becomes similar to or even larger than the axial force (Li & Liu, 2019; Zhang et al., 2023). Therefore, the shear strength of bolted rock joints varies based on the actual situations. Zhang et al. (2022) found that as the bolting angle increased, the shear strength increased rapidly. In contrast to the findings of Liu et al. (2017), Li et al. (2021), Li and Liu (2019), and Cui et al. (2020) that the shear strength first increased and then declined, Spang and Egger (1990) and Grasselli (2005) observed that the shear strength progressively decreased as the bolting angle increased (Figure 19). This was because the rock bolt's axial strength was much higher than its shear strength, and the bolting angles affected how much the axial force and shear force contributed to the shear strength. Therefore, smaller bolting angles can perform better. Thus, the smaller bolting angles can facilitate better use of the tensile strength of rock bolts.

               

               

The following parameters were used by Ma et al. (2019): ${𝑁}_{\mathrm{p}}=2\text{MPa}$ , ${𝑄}_{\mathrm{p}}$  = 1 MPa, and $\mathit{𝜗}={30}^{°}$ . As a result, Figure 20 shows the relationship between the shear strength, axial force, and bending angle of the rock bolt after failure. It could be found that for the same axial force, the shear strength first increases and then decreases with the increase of the bending angle. However, as the axial force increases, the shear strength curve only decreases with the increase of the bending angle. This explains why the shear strength versus bolting angle curves display different shapes in Figure 19, because the bending angle of the rock bolt increases approximately linearly with the increase of the bolting angle (Grasselli, 2005; Li et al., 2021; Pellet & Egger, 1996). Moreover, the bolt anchors the joint rock mass most effectively and strengthens its shear resistance when the axial force is 75%– 95% of the ultimate tensile force and the bending angle of the rock bolt is 30°–50° in an ideal state (Figure 21).

               

4.5 Future research topics

The mechanical response of joint rock with bolts has been comprehensively analyzed by many scholars, as discussed above. However, the large and shear deformation of rock bolts remains one of the most challenging problems of the tunnel reinforcement system (Chen & Li, 2015). Therefore, more research on the mechanical characteristics of bolted rock joints needs to be further conducted in the future.

The deformation and failure of deep roadways/tunnels are becoming increasingly more severe with the increase of mining depth and mining intensification (Sui, 2022a, 2022b, 2023), especially in an environment of high stress, high temperature, and high osmotic pressure (He et al., 2005). Most of the studies reviewed in this study were conducted at room temperature without taking the influence of temperature into consideration. Only Li et al. (2023) and Saman et al. (2023) performed shear testing on bolted rock joints at high normal stress (>10 MPa), and each test was conducted in a plane stress state. Not much attention has been paid to the triaxial mechanical reactions of bolted rock joints under high stress, high temperature, and high osmotic pressure. Therefore, further studies on more accurate bolted rock joint mechanics under complex situations are crucial for future deep engineering research. Moreover, the long-term interaction between rock bolts and rock fractures is complex because it depends on fracture networks as well as the characteristics of rock bolts and rock joints. However, most existing studies (Chen, Chen, et al., 2018; Chen & Li, 2015; Zhao et al., 2020) only examined the mechanical properties of one or two joints reinforced with a single rock bolt. Furthermore, grouting plays a vital role in rock joints by covering joint surfaces and preventing shear deformation (Jin & Sui, 2021). Meanwhile, subsurface water seepage could widen the joint and corrode the rock bolt, and earthquakes and other engineering disturbances could cause cyclic shear stress on the rock fracture. The reinforcing effect of rock bolts gradually decreases because of these dynamic, complex processes (Li, 2010). Moreover, due to technical limitations, researchers could only record shear/normal displacement versus shear load. However, after failing to analyze the mechanical characteristics of the bolted rock joint, some researchers also measured the strain of the rock bolt surface and the fractured rock mass on the joint surface. The deformation of cracked rock reinforced by rock bolts is uncertain. Accordingly, it is crucial to determine the mechanism of bolted rock joints in difficult conditions and develop more advanced technological tools.