## 3 Establishment of Numerical Model for Surrounding Rock of Roadway Excavation
### Construction of Numerical Models  
The 3 DEC software is a three-dimensional numerical modeling program that utilizes the discrete analysis method. It enables the simulation of the response of discrete blocks, such as jointed rock masses, under both static and dynamic loads. Consequently, 3 DEC can effectively simulate processes including block separation, rotation, and collapse, and can establish contact with and perform mechanical calculations on new blocks after their collapse [17; 18; 19]. The use of 3 DEC (3 Dimension Distinct Element Code) software allows for a more intuitive study of the stability of the surrounding rock after roadway excavation and repeated support. The numerical modeling of the advancing face was conducted using the Bonded Block Model (BBM) method with the 3 DEC software. This approach involved simulating the surrounding rock through a collection of bonded tetrahedral elements, enabling the analysis of various processes, including fissure development, fragmentation, as well as stress and strain dynamics [20; 21]. The geological numerical model of the coalfield has dimensions of 36 m \(\times\) 25 m \(\times\) 46.6 m, with a rectangular tunnel section measuring 5.0 m in width and 3.6 m in height. Considering the stepping temporary support mechanism, the influence of the support system on the roadway bottom is minimal. Consequently, the established numerical model directly merges the floor with the basic floor to form the roadway bottom. The roadway roof comprises the direct roof and the basic roof, with a coal seam thickness of 5 m. The direct roof is positioned above the excavated coal seam, while the upper part of the direct roof represents the basic roof. Coulomb sliding is employed to model the contact types between internal constitutive blocks within rock formations and between distinct rock formations in numerical simulations. The numerical model is visually depicted in Figure 8.  
The direct roof plays a crucial role in controlling the surrounding rock of the comprehensive excavation roadway. This study aims to investigate the stability of the direct roof under stepped temporary support, and evaluate the applicability of this support method through numerical simulations. By varying the thickness and mechanical parameters of the direct roof, as well as the roadway depth, different roof conditions are considered. The repeated supporting process of the stepped temporary support has minimal impact on the basic roof, floor, and coal seam of the roadway. Consequently, the basic roof and bottom plate of the roadway are considered non-control variables. The geological conditions are set as relatively hard sandstone and sandy mudstone, which remain constant throughout the numerical simulation. The model consists of individual blocks, each with a side length of 0.3 m, resulting in a total of approximately 1.55 million three-dimensional elements. To achieve a gradual mesh transition from the center to the outer side, a gradual mesh refinement approach is applied from the roof and bottom towards the center. Fixed boundary conditions are imposed on the left and right, front and back sides, as well as the bottom of the model to restrict horizontal and vertical displacements. A vertical downward load is applied to the roof of the model to simulate the self-weight stress generated by the overlying rock layer. Varying the roof loads allows for simulating the stability of the excavation roof at different depths of the roadway. During the excavation, support, and anchoring equipment processes, the cantilever shearer has a length of approximately 8-10 m, and each set of twin-link temporary support units has a width of 3.2 m. Therefore, three sets of twin-link temporary support units are used to form a temporary support zone above the shearer, creating a tunnel temporary support area.