## 1 Introduction  
Rock bolt support, as an economical and effective active support method, has been widely applied in engineering supports, such as tunnels, slopes, water conservancy and hydropower, and underground mines [1, 2]. Rock bolt support is the main support form in Chinese coal mine roadways. In the excavation of about 8000 km of coal mine roadways every year, 80% adopt rock bolt support [3]. The factors that affect the stability of the roadway surrounding rock and the effect of rock bolt support usually include water corrosion [4], the width of the coal pillar reserved [5], as well as the diameter and angle of the rock bolt installation, rock strength, grouting material, rock bolt material, drilling diameter, pre-tightening force of the rock bolt, normal stress, surface roughness of the joint, expansion angle of the joint, etc. [6, 7]. Many scholars at home and abroad have studied the mechanism and failure mechanism of rock bolts under different conditions through three aspects: laboratory tests, numerical simulations, and theoretical analyses. In terms of laboratory tests, [PERSON] et al. [8] studied the influence of the intermediate principal stress on the strength characteristics of rock bolts through true triaxial tests. The results show that as the confining pressure gradually increases from zero, the behavior of rock bolts before failure changes from linear to nonlinear. [PERSON] et al. [9] revealed the influence of adding fly ash in grouting on the axial bearing capacity of fully grouted rock bolts through rock bolt pull-out tests and uniaxial compression tests. The results show that after the addition of fly ash, the axial bearing capacity of rock bolts can be effectively improved. [PERSON] et al. [10] applied confining pressure and pull-out load in indoor tests and conducted tests on rock bolts using ultrasonic guided waves. The propagation law of ultrasonic guided waves and the bonding quality of rock bolts under the action of pull-out load and confining pressure were studied. [PERSON] et al. [11] revealed the influence of the restraint diameter on the axial bearing capacity of rock bolts through grouting solidification and rock bolt pull-out tests. The results show that increasing the restraint diameter, the bearing capacity of rock bolts increases by approximately 32% and 45% on the 7 th and 28 th days, respectively. [PERSON] et al. [12] prepared a rock bolt heating pull-out test device and studied the mechanical properties of resin rock bolts under high-temperature conditions. The results show that when the ambient temperature reaches 75 \({}^{\circ}\)C and 150 \({}^{\circ}\)C, the bonding capacity of resin rock bolts decreases by 6.6% and 31.3%, respectively. In the field of numerical simulation, [PERSON] et al. [13; 14] conducted a large number of anchorage shear laboratory tests on 2G-NPR rock bolts. A three-dimensional refined numerical simulation method considering the elastic-plastic mechanical behavior of rock mass, the tensile-shear fracture criterion of rock bolts, and the damage and deterioration of the grouting body was proposed. [PERSON] et al. [15; 16] analyzed the influence of different parameters of the anchor bolt on its ultimate bearing capacity through the finite element analysis software ABAQUS/Explicit. It is indicated that in the environment where the roadway is in a layered composite roof and under impact ground pressure, flexible bolts can play an important role due to their strong ability to resist dynamic loads. [PERSON] et al. [17] used the PFC simulation method to study the macroscopic shear behavior and microscopic failure characteristics of a single rock bolt under different types of rock joints. [PERSON] et al. [18], based on the failure theory of rock bolts, modified the mechanical model of the pile element in the FLAC\({}^{3D}\) program and revealed the distribution and evolution characteristics of the axial force and shear resistance of rock bolts. From the perspective of theoretical analysis, [PERSON] et al.