## 1 Introduction  
Natural rock masses generally contain joints, the presence of which play an important role in the mechanical properties of rock masses. Research on the failure behaviour of jointed rock masses has always been an influential field in rock mechanics. Typically, rock joints are classified as penetrating and nonpersistent joints. The mechanical properties of nonpersistent joints in uniaxial compression have been one of the fundamental issues in the research of the mechanical behaviour of jointed rock masses. [PERSON] and [PERSON] [1] first studied the failure characteristics of joint specimens under uniaxial loading. After that, many scholars carried out experimental and theoretical derivation research in this field. [PERSON] et al. [2] performed uniaxial compression on intermittently prefabricated fractured marble to probe the impact of the geometric distribution on the deformation and failure characteristics of marble. [PERSON] et al. [3] studied the deformation and failure mechanismsof nonpenetrating rock masses under uniaxial compression from the perspective of energy evolution. [PERSON] et al. [4] established a dynamic failure intrinsic model of nonpersistent jointed rock masses with uniaxial compression based on the Taylor-Chen-Kuszmaul (TCK) model. [PERSON] et al. [5] established an elastic-plastic fracture model of nonpersistent jointed rock under ballast action on the basis of the Drucker-Prager (D-P) criterion. [PERSON] et al. [6] performed uniaxial loading of gypsum specimens containing double prefabricated cracks, and based on a modified maximum strain energy release rate criterion (G-criterion) and displacement discontinuity method (DDM), crack propagation and incorporation behaviour were predicted. [PERSON] et al. [7] carried out uniaxial and biaxial tests on prismatic specimens under parallel double cracking to investigate crack propagation and coalescence processes and found that the geometry of the crack and the surrounding compressive stress play an important function in crack evolution. Apart from specimens with joints in two dimensions, a small number of scholars have also carried out experimental and numerical simulation research on three-dimensional joints. For example, [PERSON] et al. [8] investigated the mechanism of three-dimensional crack development during uniaxial compression by fabricating and uniaxially compressing specimens containing a single prefabricated fracture-like rock, and they concluded that the individual presence of cracks has a limiting effect on the three-dimensional propagation of wing cracks. [PERSON] et al. [9] investigated crack initiation, wrapping and coalescence in specimens with 3D cross-embedded flaws under uniaxial compression. Based on uniaxial tension tests on precracked rock-like specimens, [PERSON] et al. [10] fabricated red sandstone specimens containing two unparallel cracks and characterized the crack evolution of the specimen with different crack inclinations under uniaxial loading. In contrast to laboratory tests, numerical simulations are utilized to simulate the failure processes of jointed rock due to their economical properties. For the rock fracture process, particle flow code (PFC) has been the most popular simulation method in the past ten years. Based on PFC2D and the parallel bonding model, [PERSON] et al. [11] explored the effect of joint overlap on the shear failure mechanism of rock bridges from both macroscopic and microscopic perspectives. By using PFC2D, [PERSON] et al. [12] investigated the fracture behaviour of red sandstone specimens with nonparallel flaws under uniaxial compression, and the fracture behaviour during deformation was analysed and discussed. [PERSON] et al. [13] simulated the peak strength and failure characteristics of multifractured rock materials under uniaxial loading by PFC2D and classified the failure modes of multifractured specimens into four categories. [PERSON] et al.