## 7 Numerical Simulation of the Blasting-Induced Damage in Rock  
### Design of the Test Schemes  
In order to study the development pattern of rock mass damage zone after blasting under different lateral pressure coefficients, and compare it with the damage propagation law of microcracks in physical model experiments, numerical simulation of blasting damage was carried out. Numerical simulation of the dynamic load during blasting is undertaken using FLAC\({}^{\text{3D}}\) finite element software. The model measured 300 mm \(\times\) 300 mm \(\times\) 250 mm (length \(\times\) width \(\times\) height) and a pre-cut blast hole with a length of 10 mm and diameter of 8 mm was located at the centre of the model, some 123 mm from the top surface of the model. A three-dimensional geometric calculation model is established in FLAC\({}^{\text{3D}}\), in which a total of 159,744 elements are used (Figure 12)  
It is necessary to find the related dynamic parameters and dynamic mechanical characteristics of rock at different loading rates when performing blast tests on rock in a high-stress environment. It is feasible to employ the formula for the dynamic compressive strength recommended by [PERSON] et al. [25] when the strain rate on such rock materials exceeds 30 s\({}^{-1}\). \[\sigma_{\text{cd}}=0.4\sigma_{c}(\xi)^{1/3} \tag{4}\]  
where, \(\sigma_{c}\) and \(\xi\) refer to the uniaxial compressive strength (MPa) and the strain rate (s\({}^{-1}\)), respectively. Owing to the strain rate around the blast hole for explosive charging being between 10\({}^{3}\) to 10\({}^{5}\) s\({}^{-1}\), a strain rate of 10\({}^{4}\) s\({}^{-1}\) is used here. The dynamic elastic modulus is generally larger than the static elastic modulus of rock. The relationship between the dynamic and static elastic moduli of rock is given by [PERSON] et al. [26]:  
\[E_{dyn}=\left(E_{s}/10^{0.02}\right)^{1/0.77}/\rho_{i} \tag{5}\]  
where, \(E_{s}\), \(E_{dyn}\), and \(\rho_{i}\) represent the static elastic modulus (GPa), dynamic elastic modulus (GPa), and density (g/cm\({}^{3}\)), respectively. When calculating the dynamic mechanical parameters of rock, it is necessary to calculate dynamic mechanical parameters of rock blocks and then compute mechanical parameters for the rock according to the modified Hoek-Brown formula. The simulation materials selected are only used to reveal the specific same test law. Because granite has the characteristics of compact structure, high compressive strength, low water absorption and high hardness, it is found that the damage area of granite after blasting loading is obviously expanded through numerical simulation comparison of various materials, which is the best match with the physical experiment results, so granite is selected as the numerical simulation model material. Granite is our chosen materials for testing and its dynamic and static mechanical parameters are summarised in Table 3.  
It is experimentally supposed that the pressure is directly applied to the wall of the blast hole and the radius of the damage zone is mainly determined by the pressure applied thereto, therefore, the calculation method and loading path of the pressure on that wall are the key to numerical simulation of blasting. The pressure function initially introduced by [PERSON] and [PERSON] and then modified by [PERSON] et al. [27] is taken as the stress wave to simulate the time-history loading path of the dynamic pressure:  
\[P_{t}=4P_{b}\left(e^{-\beta t/\sqrt{2}}-e^{-\sqrt{2}\beta t}\right) \tag{6}\]  
where, \(P_{t}\), \(P_{b}\), \(\beta\), and \(t\) refer to the change in the pressure (Pa) on the blast wall with time, the pressure (Pa) applied thereto, the damping coefficient (1/s), and the action time (\(\upmu\)s),