## Materials and Methods
### Numerical Simulation Model Construction  
#### 2.3.1 Numerical Model Parameter Validation  
During the process of a numerical simulation, the selection of reasonable physical and mechanical parameters can allow the simulation to effectively reproduce the rock's mechanical behavior. In order to determine physical and mechanical parameters of the blocks and joints of the model, the previous methods are selected to check the parameters [30; 31; 32; 33], and the numerical simulation is fitted with the data of the Basic Mechanics experiment (compressive experiment and tensile test), in the simulation process, according to the failure criterion of the joint, as shown in formulas (1) and (2). A 'FISH' program is used to determine whether the joint is broken when the joints have tensile damage. The broken joints are classified into the \"tensile damage\" group, and when the joints produce shear damage they are allocated to the \"shear damage\" group; the number of broken joints in each group is recorded separately. The dimensions of the rock sample for compression test is \(50\times 100\) mm (diameter \(\times\) height). Udec software was used to establish a two-dimensional numerical model with dimensions of \(50\times 100\) mm (width \(\times\) height). The experimental results of the uniaxial compression test and the numerical simulation are shown in Figure 6. An \"X\"-shaped form of destruction is present on the specimen when the rock specimen is destroyed (Figure 6a). The same failure mode is also obtained in the numerical simulation, as shown in Figure 6b. Figure 6c is the stress-strain curve of the uniaxial compression test of the model. The stress peak of the specimen's uniaxial compression is 75.03 MPa. In terms of stress peaks and stress curves, the results of the numerical simulation show good consistency with the experimental data. The damage percentage is the number of damaged joints divided by the total number of joints before reaching the peak stress of 65%. The joints mainly show tensile failure beyond  
Figure 5: Relationship between the normal stress and hydraulic aperture of the joints. this stress value. The joints start to produce shear damage, and the amount of destruction rapidly increases when peak stress is reached. The percentages of joints damaged due to shear and tensile are 20% and 15%, respectively, after the peak stress. The shear failure is stable at 42%. The tensile failure is stable at 17%. Nearly 59% percent of the joints in the model are destroyed. The rate of shear damage is ~2.5 times the rate of tensile failure. The dimensions of the rock sample for tensile testis is 50 \(\times\) 25 mm (diameter \(\times\) thickness). A two-dimensional numerical model with diameter of 50 mm is established with Udec software. The tensile fractures in the numerical simulation are presented as straight lines throughout the specimen, as shown in Figure 7b, which is consistent with the damage pattern obtained by the laboratory test, as shown in Figure 7a. Figure 7c is the stress-strain curve of the tensile test of the model. Before the stress peak, the stress increases linearly with the increase in strain. A \"cliff-type\" drop in stress values occurs after reaching the stress peaks. The numerical simulation results and laboratory results correlate well. In the curve, it can be seen that tensile failure is the main failure form in the tension experiment, and when the stress reaches the peak stress level of 25%, tensile damage gradually starts, and after the peak, the number of joints with tensile damage is stable at ~16.7% after a sharp increase. Nearly 17.5% of the joints in the model are damaged, and only a small number of joints show shear damage. Figure 6: Calibration of the numerical model to the uniaxial compression tests: (a) failure pattern of the laboratory sample; (b) failure pattern of the numerical model; and (c) stress–strain curve of the numerical model.