## 1 Introduction
It has achieved good results in complex and difficult conditions such as high geostress roadways, soft rock roadways, roadways affected by strong dynamic pressure, and roadways digging and staying along the empty roadways in kilometer-deep wells [17; 18; 19; 20; 21; 22]. Its working principle is to fully utilize and improve the bearing capacity of the rock body, which has a good reinforcement effect and economic cost [23; 24; 25]. In recent years, many scholars at home and abroad have explored and researched the action mechanism of anchors from various aspects, including some classical theories such as suspension theory, combined beam theory, combined arch theory, perimeter rock loosening circle support theory, and perimeter rock strength reinforcement theory [26; 27]. The research methods are mainly divided into indoor tests, model tests, theoretical analysis, and numerical simulation. [PERSON] et al. [28] investigated the reinforcing effect of anchors on rock bodies containing penetrating fissures under uniaxial tensile conditions through indoor experiments, and the results showed that the anchored specimens showed plastic damage characteristics and the anchors increased the deformation modulus and uniaxial tensile strength of the jointed rock body. [PERSON] and [PERSON] (1998) and [PERSON] et al. (2001) conducted experiments on rock-like materials containing two and three fissures (rectangular specimen dimensions: 60 \(\times\) 120 \(\times\) 25 mm) subjected to uniaxial compression. Their findings revealed that the peak strength of the specimens was not contingent upon the initial crack density but rather on the actual number of pre-existing flaws involved in the coalescence process. [PERSON] et al. [29] carried out tensile-shear tests on the anchored specimens by developing a new test method to characterize the strain distribution of the surface of the anchors under the tensile-shear loading and, at the same time revealed that the angle of the installation of the anchors. In a separate study, [PERSON] and [PERSON] [30] examined a series of specimens (rectangular specimen dimensions: 101.6 \(\times\) 203.2 \(\times\) 30 mm) composed of gypsum and featuring three and sixteen fissures, which were subjected to uniaxial compression. Their research focused on elucidating the influence of continuity and the ligament influence of continuity and ligament length on the stress associated with crack coalescence. [PERSON] et al. [31] simulated the formation process of rock bodies in fault-fracture zones by a novel test method and prefabricated model specimens of anchors anchored by uniaxial. The effect of the anchorage form on the bearing capacity and damage mode of the fault fractured rock body was investigated by compression test. [PERSON] et al. [32] investigated the effect of the nodal angle and anchor density on the anchorage strength, deformation behavior, and axial force evolution characteristics of the anchorage in the model specimen under the action of normal stress by prefabricating a large-scale nodal model specimen (500 mm\(\times\)500 mm\(\times\)480 mm). With the continuous development of advanced testing techniques and computer simulation software, unprecedented progress has been made in recent years in the study of anchor support principles. [PERSON] and [PERSON] [33] introduced a doubly enriched finite element (DEFE) procedure designed for simulating grouted bolts passing through rock joints. [PERSON] et al. [34] incorporated a rock bolt element, grounded in analytically derived interface behavior, into a two-dimensional discontinuous deformation analysis (DDA) program to assess the effectiveness of the rock reinforcement system, yielding valuable insights into the role of DDA in the design of rock reinforcement systems. [PERSON] et al. [35] constructed a three-dimensional bolt-reinforced model within rock joints using the FLAC3D numerical calculation program. They investigated the influence of bolt inclination angles on both flat and undulating joint surfaces.