# Improved Block Element Method for Simulating Rock Failure
## 5 Numerical Simulation and Discussion
### Sensitivity of Mesoscopic Parameters on Rock Failure Behavior  
The damage evolution constitutive model proposed in this study includes four key failure parameters, including tensile strength, shear strength, normal fracture energy, and shear fracture energy. These parameters collectively govern the damage evolution process and the ultimate failure mode of the material under complex stress conditions. To establish a rational parameter selection methodology and to better understand the mechanical influence of each parameter, this section conducts a sensitivity analysis focusing on the effects on the failure characteristics of rock. In terms of methodology, the control variable approach is employed. While keeping the other parameters constant, uniaxial compression numerical simulations were conducted by varying the tensile strength (15 MPa, 12 MPa, and 9 MPa), shear strength (104 MPa, 83.2 MPa, and 62.4 MPa), and fracture energy (1, 1.5, and 2 times the initial value). The loading and boundary conditions in the numerical simulations were consistent with those described in the previous section. The failure patterns of the specimens obtained from the sensitivity analysis are similar to those shown in Figure 12. Figures 13-15 present comparisons of the compressive stress-strain curves with different parameter combinations. Figure 14: Stress-strain curves under uniaxial compression with different mesoscopic shear strengths. Figure 15: Stress-strain curves under uniaxial compression with different mesoscopic fracture energies. 1. The sensitivity analysis of the mesoscopic tensile strength indicates that when the tensile strength varies within the range of 9-15 MPa, the peak compressive strength of the specimen fluctuates by only about 3%, and the overall shape of the stress-strain curve remains nearly unchanged. This indicates that under uniaxial compression, the rock failure process is primarily governed by shear mechanisms, and the influence of the mesoscopic tensile strength parameter is negligible;
2. The influence of the mesoscopic shear strength exhibits a completely different macroscopic compression strength. As the shear strength increases from 62.4 MPa to 104 MPa, the peak compressive strength rises markedly from 135.4 MPa to 196.1 MPa, representing a 44.8% increase. This trend can be explained by the fact that a higher mesoscopic shear strength enhances the resistance to sliding along block interfaces, thereby significantly improving the overall load-bearing capacity;
3. Mesoscopic fracture energy affects both the softening segment of the stress-strain curve and the overall strength, but it has little impact on the pre-peak portion of the curve. As the mesoscopic fracture energy increases, the softening segment of the stress-strain curve becomes more gradual. Additionally, a higher mesoscopic fracture energy leads to an increase in macroscopic compressive strength, though the degree of improvement is relatively limited. These findings validate the rationality of the parameter settings in the proposed constitutive model and also provide a theoretical basis for parameter selection in engineering applications. Although the mesoscopic tensile strength has a relatively limited effect on the compressive performance of the specimen, it plays a decisive role in governing the macroscale tensile mechanical behavior. To clearly demonstrate this characteristic, a series of uniaxial tensile simulations are conducted in this section as well. The tensile simulations used the same model dimensions and displacement boundary conditions as the previously described uniaxial compression tests. Keeping all other material parameters constant, different macroscopic tensile strength values (15 MPa, 10 MPa, and 5 MPa) are assigned to investigate the influence of the tensile strength on the specimen's tensile performance. Figure 16 shows the uniaxial stress-strain curves and failure patterns under different tensile strengths. 1.