# Numerical Modeling of Engineering-Scale Jointed Coal Mass and Confining Pressure Effect
## 1 Introduction  
Joints frequently occur in coal seams, which are a kind of special structural plane formed during geological tectonics and sedimentary coalification. Joints in coal seams can be divided into bedding and cleat, and their structural characteristics and mechanical parameters are the basis for investigating the dynamic response of coal mass [1; 2; 3; 4]. Typically, bedding and cleats are vertically distributed to form a complex joint network in coal seams. These structural planes, including bedding and cleats, lead to distinct disparities in the mechanical response and failure mechanisms between jointed and intact coal masses [5; 6; 7; 8]. The prerequisite for modeling the joint discrete fracture network (DFN) in coal masses is to obtain the distribution parameters of joints. As a special kind of structural plane, joints are suitable for existing statistical sampling methods of the structural planes. The structural plane parameters involve descriptors such as spacing, aperture, persistence, roughness,filling condition, number of sets, and block size [7; 9; 10; 11]. Simulation of a joint network was first proposed by [PERSON] and [PERSON] [7; 12], which was later developed and refined by [PERSON] [13]. The simulation primarily encompasses four stages: joints sampling, delineation of dominant joint sets, determination of probabilistic models, and model construction with parameter verification. The sampling techniques are categorized into two types: the measurement window method and coal/rock core statistical analysis, which can be executed using equipment such as compasses, cameras, and total stations [14; 15]. The results of joints sampling often encompass multiple dominant sets based on their attitudes [16], such as bedding and cleats in coal seam. Subsequently, for each delineated set of joints, the probabilistic distributions governing their geometric parameters, including the dip direction, dip angle, and spacing, are statistically analyzed [17; 18]. Ultimately, numerical software is utilized for model construction and the calibration of simulation parameters. The common methods for coal/rock joint network construction include Interface command in FLAC [19; 20], joint command in UDEC/3 DEC [21; 22; 23; 24], cohesive element method [11; 25; 26], and smooth-joint DFN in PFC [27; 28; 29; 30; 31]. In contrast, the particle discrete element method eliminates the need to preset constitutive relations for the coal rock mass. It can directly represent the coal rock model using a number of particles and contact models, making it well suited for studying the mechanical properties of engineering-scale coal masses that contain numerous joints. When studying the mechanical properties of coal/rock using PFC, [PERSON] et al. [27] investigated the effects of the spacing and dip angle of joints on the mechanical properties and failure modes of the interrupted jointed rock mass under the uniaxial compression condition. [PERSON] et al. [32] obtained the strength and the deformation failure characteristics of the rock under the true triaxial stress condition. [PERSON] et al. [33] analyzed the mechanical and failure behaviors of anisotropic gneiss under a triaxial geostress environment by PFC3D simulations. [PERSON] et al. [34] conducted uniaxial and triaxial compression tests on rock specimens with prefabricated fissures using the particle discrete element method. They analyzed the strength characteristics and crack propagation behavior of the rock under varying fissure dip angles and confining pressures. [PERSON] et al. [35] constructed a true triaxial numerical model of sandstone by using PFC3D, and revealed the effects of intermediate principal stresses on the peak stresses, the deformation modulus, the relationship between brittleness and ductility, and the failure mode of the rock. The research results of [PERSON] revealed that the strength of the specimen decreased in a nonlinear manner when the joint density increased [36], and the distribution of the joints determined the failure mode of the coal rock.