## 2 Establishment of a Method for Evaluating Rock Damage Effects
### Determination of Evaluation Indicator Thresholds
#### 2.2.2 Damage Factor Threshold  
The damage effect of rock mass in PD partition is evaluated by the damage variable. Equations (9) and (10) represent the relationships between the damage variable, acoustic wave velocity, and elastic modulus:  
\[D=1-E/E_{0} \tag{9}\]  
\[E=\rho v^{2}(1+\mu)(1-2\mu)/1-\mu \tag{10}\]  
where \(E_{0}\) is the original elastic modulus, \(E\) is the post-blast elastic modulus, and \(v\) represents the post-blast rock longitudinal wave velocity. After blasting rock wave velocity reduction rate \(\eta\): \(\eta=1-v/v_{0}\), density and Poisson's ratio before and after the blast is approximately equal. Equation (11) for the damage variable \(D\) is obtained from Equations (9) and (10).  
\[D=1-(v/v_{0})^{2}=1-(1-\eta)^{2} \tag{11}\]  
Using the acoustic testing method to measure the wave velocity of the rock mass before and after blasting, obtain the value of the damage variable \(D\), and then determine the degree of deterioration of the rock mass under the action of blasting. By pertinent national regulations, when the damage variable \(\eta\) exceeds 10%, the rock mass initiates damage, with a corresponding threshold value of 0.19. Through statistical analysis of empirical data from domestic and international sources, researchers determined a damage threshold range between 0.75 and 0.85 for complete rock mass failure [32]. This study adopts a damage variable threshold of 0.75, even under adverse conditions.  
Based on the above analyses, the tensile stress area (PT partition) and the complex action area of the hole loading section (PD partition) use different indicators to evaluate the blasting damage effect of the rock. The peak tensile stress \(\sigma_{tmax}\) of the monitored cell is output in the PT partition, and the peak damage variable \(D_{max}\) is output in the PT and PD partitions. The relationship between the peak tensile stress \(\sigma_{tmax}\) of the monitoring unit and the peak damage variable \(D_{max}\) with the depth of the blast hole are plotted separately to evaluate the damage effect of the rock at the monitoring unit. It is important to note that under the effect of blasting, rocks are damaged in block form. If the monitoring unit is located on a fractured rock block, the \(D_{max}\) value may be less than the damage threshold of 0.75. To quantitatively describe the rock damage in the region, the ratio of the interval length with a damage variable greater than 0.75 to the total partition length was defined as \(C_{D}\), and the variance of the damage variable, \(D_{(CD)}\), was used to comprehensively evaluate the effect of rock damage under different loading configurations in the case of similar \(C_{D}\) values. The larger the \(C_{D}\) value, the more energy the explosive allocates to destroy the rock; the smaller the \(D_{(CD)}\) value, the more uniform the energy distribution. In the PT partition, due to the insensitivity of the HJC material model to the damage caused by tensile stress, it is necessary to combine \(D_{max}\) with \(\sigma_{tmax}\) to make a comprehensive judgment on the damage to the rock. When \(\sigma_{tmax}\) is greater than the dynamic tensile strength of the rock, the rock damage can be judged visually. The composite index replaces the single damage evaluation index in the crushing zone and fracture area, and the damage of the rock at the fuzzy boundary of the two parts can be accurately judged.