## 3 Creation of a Numerical Model of Basalt
### Establishment of an FDEM Model of Basalt Rock Mass of an Underground Powerhouse  
Based on the actual in situ situation of Baihetan Hydropower Station, a 2D FDEM model of a typical section of the left-bank underground powerhouse was established, where only the intact basalt rock mass containing hidden cracks was considered, as shown in Figure 9. This model considers the excavation of an arched tunnel with dimensions of 34 m \(\times\) 88.70 m, located at the center of a 400 m \(\times\) 400 m square area, and the size of the model on one side is made 3-5 times the excavation span to minimize the boundary effects. Based on the damage degree and range during rock mass excavation, the model can be classified into three sub-regions with varying degrees of mesh precision. The excavation area (i.e., Region A) was located in the innermost region, whose element size is in the range of 0.5-2 m. The excavation-affected area or interest area (i.e., Region B) with dimensions of 200 m \(\times\) 200 m that was expected to be fractured was set around the excavation area, with an element size of 0.5 m, and this size was equal to the REV size of the basalt block with hidden cracks. For the non-excavation-affected area or general consideration area (i.e., Region C), where fracture was not expected to occur, the element size was set to a range of 0.5-5 m. Thus, a balance between the computational cost and element suitability required in the numerical simulation to capture the fracture process of the basalt rock mass of underground caverns could be achieved.  
Based on the actual in situ stress conditions measured at the engineering site, the primary stress field applied to the numerical model was \(\sigma_{1}=-23\) MPa, \(\sigma_{3}=-12\) MPa, in which the negative sign indicated that the ground stress was a compressive stress, and a plane strain condition was adopted. A zero-displacement state was used around the outer boundary of the numerical model to simulate the far-field conditions; that is, the horizontal and vertical directions were fixed. During the excavation of the underground caverns, a tunnel face replacement method was used to simulate the 3D effect of tunnel face advancement; that is, the gradual unconstraint of the rock mass due to the tunnel face advancement was captured by gradually reducing the Young's modulus of the core material from the initial value to zero in the tunnel excavation area, thereby completing the removal of materials in the excavation area. In this model, all the regions containing only hidden cracks were implicitly characterized by the equivalent mechanical parameters of the REV-sized basalt blocks, and a series of checks were performed to ensure that the numerical simulation could accurately reproduce the mechanical response characteristics  
Figure 9: FDEM model configuration of the left-bank underground powerhouse at Baihetan Hydropower Station.  
at the engineering site during the excavation of the underground rock mass, including the deformation, failure characteristics, and extent of the damage area. Table 1 presents the corresponding FDEM model parameters. The total number of simulation time steps was 3 million; each time step was 1.5 \(\times\) 10\({}^{-6}\) s, and the output frequency of the numerical results was 10000 steps, regardless of the gravitational acceleration.