## 1 Introduction  
Since the beginning of the 21 st century, the number and the scale of tunnels and underground projects in China have achieved unprecedented development, and the engineering construction conditions and geological environment have become more and more complex. In particular, the large-scale urban underground traffic construction has brought many new challenges to construction safety and operation safety, and has become a scientific problem that needs to be solved urgently in the construction of underground projects. Some scholars pointed out that the safety assessment of tunnel stability is crucial to tunnel construction, and accurate analysis can lead to reliable predictions [1; 2; 3; 4]. Under the guidance of the NATM theory, China has formed a variety of tunnel support concepts and technologies. In general, the tunnel support method has gradually changed from single support to combined support. The support concept has also changed from emphasizing the role of secondary lining support to paying attention to the primary support to bear the load of surrounding rock, and the secondary lining is only used as a safety reserve. The combined support type composed of a grid arch, anchor bolt, and shotcrete is a widely used flexible support type, which can maximize the self-bearing capacity of the surrounding rock and allow appropriate deformation of the surrounding rock. Many scholars at home and abroad have carried out in-depth research on the bearing mechanism and support performance of grid arches, and have reported a series of achievements. [PERSON] and [PERSON] [5] took the lead in designing a three-limb grid arch, and verified the rationality of the structural design, combined with field application tests. [PERSON] et al. [6] conducted an in-depth analysis of the mechanical characteristics of the three-limb grid arch, and expounded the mechanical response under different parameters. [PERSON] et al. [7] analyzed the differences in ultimate bearing capacity and structural stability between the new four-limb grid arch and the three-limb grid arch through indoor tests and numerical simulations. [PERSON] et al. [8] carried out research on the mechanical properties of a high-strength grid arch, obtained reasonable structural design parameters, and the good stability and bearing performance of this structure are verified. [PERSON] et al. [9] presented an evaluation of the structural performance of tetragonal lattice girders for NATM tunnel construction, and evaluated the ultimate carrying capacity and checked the rationality of the connection method of the girder. [PERSON] et al. [10] evaluated the relationship between the ultimate bearing capacity of a four-limb grid arch and its component cost, and systematically studied the influence of factors such as web bar diameter and weld length on the mechanical properties of the grid arch. [PERSON] and [PERSON] [11] carried out a field test of heat-treated high-strength lattice girders in railway tunnels and highway tunnels, compared the support performance with the original-design I20b steel arch, and achieved good application results. [PERSON] et al. [12] and [PERSON] et al. [13] studied the mechanical properties of concrete segment joints of different materials in shield tunnels, verified the design method, and conducted in-depth research on the waterproof performance of different joints. Rigid support structures are usually used to bear strong loose ground pressure, such as concrete-filled steel tubulars [14], prefabricated arc plates [15], spatial reticulated grids [16; 17], high-strength shotcrete [18], high-strength pre-stressed anchors [19], pretensioned bolt-cable cooperative support [20], etc. It is highly necessary to control the deformation of the deep weak surrounding rock by erecting a supporting structure with high rigidity and high strength.